My graduate degree, despite being in management, is actually from an international relations school. I therefore have more than a bit of knowledge about IR theory and how interstate relations have played out and how international organizations like the UN, WTO, and IMF fit into the international relations rubric.
Basic Introduction to International Relations and Theory
The first, most important thing to remember about international relations is that states exist in the state of anarchy. And all states today are defined by the "Westphalian system" which was derived from a peace treaty signed in the 17th century that essentially established the modern sovereign state. All states were, by nature, independent from others, and under no other jurisdiction than their own. That is not to say that there is no international structure, but as Hobbes would say, there is no "sovereign" above them to enforce international law. Therefore, all states are necessarily self-interested (though different schools approach this differently.) All international law exists solely at the whim of the states that agree to be bound by it.
There are two main schools of thought in modern Western IR theory: realism (neo-realism) and liberalism. I am most strongly associated with realism. Other schools of thought include constructivism, Marxism, feminism (relatively new in IR), green theory, functionalism, and a few others that I know even less about. I'll mainly address realism and liberalism because they, for better or for worse, dominate most IR today.
Machiavelli was a realist way before it was cool.
"Realism" and its many sub-forms (neo-realism, classical realism, liberal realism) basically posits that all states exist as self-interested actors in accordance with international anarchy. Realists tend to see all state interactions as zero-sum and in terms of relative gains. Therefore, all states and state actors necessarily act only with their own interests at heart. Remember your Hobbes, where he argued that without a sovereign above two actors to enforce a contract, the contract was meaningless? Realists are basically Hobbesian thinkers. I'm Hobbesian myself. This is not to say that realists believe that states can't work toward complementary goals, but they always default toward states being self-interested.
Realists believe strongly that states are the most important actors in international relations (therefore diminishing the role of non-state actors like the UN or the WTO.) Realists would argue that without a higher power enforcing UN or WTO resolutions, states have no rational reason to follow them. They tend to lean toward bilateral (two state) brokering as being effective. My opinion is that realists get it right on security (SALT worked because the US and USSR enforced it on each other), but not on trade (states regularly submit to WTO and IMF rulings despite having the power to ignore them.)
Realism arguably has had the best predictive power in security-related issues in the past 50 years or so. Realist theory is, in my opinion, unparalleled in predicting how militarily opposed states will act when there is the perception of a threat or an imminent threat. It is far weaker at prediction state behavior with regards to international non-state actors, because it by nature diminishes not-state actors.
A little not-so-secret: most IR wonks in power circles like DC or London or even Tokyo are neo-realists. I also knew many future Beijing wonks who studied neo-realism at US policy programs so they could go back and use it ostensibly against American interests. Realism has a lot of sway in political circles with regards to IR. I'm not convinced this is a good thing, as liberalism would say it leads to self-fulfilling prophecies.
That said, the fact that the US and China can basically ignore most of the world and do what they want proves Thucydides (arguably the first realist!) right: the strong do what they will, and the weak suffer what they must.
On the other hand, realism failed spectacularly at predicting the continual endurance of the EU and the US-Japan relationship. Realists figured that after the USSR fell, European states would have no reason to remain dependent upon each other and would once again act self-interested as they did prior to the Cold War. They were largely wrong. The same went for Japan.
Woodrow Wilson was kind of an asshole, but he was also one of the first truly idealistic international relations scholars in the United States. Credit where credit is due, I suppose.
Liberalism believes that states are (or should be) more concerned with relative gains than absolute gains. They argue that states will take risks for large gains. So, for instance, the US regularly sells some of its best military technology to allies (and even marginal allies) for both economic gain. While this puts incredible weapons in the hands of countries that could, at any point, use them agains the US, the absolute gains for everyone are greater than the absolute costs. Som in realism would argue that the US would/should never sell F-35s to Japan, since Japan could ostensibly become a hostile state gain. Liberalists would say, "the economic gain is greater than the military risk." Furthermore, liberalists argue fairly convincingly that democratic states are far less likely to go to war with one another. So far so good.
Liberalists argue, convincingly I might add, that transnational organizations like international corporations act as important non-state actors removed from the traditional Westphalian structures. Liberalists further argue that states have non-military means of interactions that sometimes take precedence. The US and the UK, for instance, haven't used military threats against one another for almost a century, instead preferring to argue with trade tools. Modern state interdependence reduces the role of military power in deciding international relations. In other words, "even in an anarchic system of autonomous rational states, cooperation can emerge through the building of norms, regimes and institutions."
Seriously, the EU shouldn't even exist. It's like a miracle and a rarity had a baby.
Constructivism is a relatively newer school of thought in IR, with a focus on the notion that a lot of how states interact is based on social constructs, rather than some defined rule. Constructivism, in short (and because I'm least-versed in it), argues that states "construct" most of the situations that they find themselves in, rather than responding to some "higher order of international anarchy."
Constructivism is fantastic at explaining things like the EU, but I am skeptical of its ability to be predictive in regards to non-state actor roles vis-a-vis powerful state actors.
Why does any of this matter?
League of Nations 2.0? More like the next Donald Trump land grab, AMIRITE?!
In short, these theories drive how states view interstate relations and non-state actors. Part of the reason why the UN is so toothless in regards to many of its sweeping resolutions is because states do not submit any authority to the UN. Realists would say that it's because states are self-interested, liberalists would say that states don't see the opportunity for absolute gains, and constructivists would say that it's because the social and political constructs don't favor adherence to this non-state actor's agenda. Regardless of how the theory explains it, the fact remains that the UN is toothless.
This is why I so often shrug my shoulders when major states with an otherwise significant interest in human rights ignore the UN. Let's say that every major state signs on to a UN resolution to ban political prisoners. And then China, being China, takes political prisoners. What do we do? Go to war with China and cost millions or billions of lives? Do we slap China with sanctions and sink our own economies? Do we send them angry IMs saying, "Y U DO THIS, CHINA-BRO?!" China will basically tell you to piss off and be done with it (as the US and every other state does when it suits them.)
Does this mean the UN is meaningless? No, not really. While the UN doesn't actually do much in the way of enforcing international law, it remains a vitally important organization for interstate communication and social construct building. The UN International Panel for Climate Change (IPCC), for instance, has been vitally important in communicating the challenges of climate change. Without the UN, states would have a harder time agreeing upon reactions to "rogue" actors like North Korea— arguably the UN is what allows the US to side with China against one of China's allies despite China having doubts about the US's motives in the region.
So the UN is important. For instance, the UN brings to light many women's issues worldwide, including women's rights, trafficking, and a wealth of data regarding women's well-being worldwide. Without the UN, "international anarchy" would be worse than it already is. The UN allows states to communicate, produce structures like the WHO that benefit billions worldwide, and disseminate massive amounts of important data. So even if the UN doesn't have the power to enforce a resolution here or there, don't throw the baby out with the bathwater. The UN is, in international terms, a relatively new experiment. And, despite the US's recent (always?) recalcitrance toward it, it remains one of the greatest triumphs of the post-WW2 regime largely put in place by the US.
However, the UN fails because states are still unwilling to give up what they view as basic powers they need to act within the international sphere. To make matters worse, in situations like the Kyoto Protocol, states may decide to not join because they feel that other actors may lead to failure (the US argued that China and India would be unable to curb emissions, and that the exceptions that the EU allowed them rendered it meaningless), leading to prisoner's dilemmas. Frankly, if a state believes that a UN agreement will likely fail due to another state, and if the state believes the UN has no power to enforce (it doesn't), then UN accords are rendered meaningless.
See where I'm going here? Because states don't believe in the motives of other states, then they doubt the efficacy of joining agreements that depend upon the motives of other states. So even if a state may actually ostensibly agree with a UN resolution, it may abstain from it, and do so rationally. This is especially a problem with human rights resolutions lately with China and other non-democratic states joining them— why should other states sign a resolution that will be conveniently ignored by Beijing or Damascus?
So, continue to support the UN and hope for countries to stay involved. Just don't expect miracles. We still have a long way to go.