Let's start with the fact that "warming" is the wrong term to use (which is why people use the term "climate change" now). It's not really warming. It's energy retention. Warming is just one side effect of the atmosphere retaining more energy.
There are a lot of feedback loops and redundancies built into the world's natural ecosystem. You see it on a small scale, where a bloom of certain resource results in a bloom of the consumers of that resource, followed by over-consumption which results in the decline of the consuming population. On the large scale, there is the same type of feedback loop that's made up of multiple smaller ones.
Right now, what's happening is that these feedback loops are handling a good chunk of the extra energy retained by CO2 so that actual atmosphereic warming is not terribly pronounced. But there's a tipping point. Once the amount of energy exceeds the capacity for these feedback loops to handle, it's going to shut down, and the moderating factor suddenly ceases to exist. The precise points are uncertain, but we know it'll happen based on what we see happening in smaller systems. For example, as prey increases, predators will also increase. This results in prey decline and then predator decline. But if due to external circumstances, the predator population grows out of control, or the prey population is completely decimated, both predator and prey (whichever wasn't affected by the initial event) will die off.
The real open questions today involve when things will happen, and how bad they'll get when these things do happen. For example, if one system fails, it can cause a domino effect on all the other feedback loops and cause them to fail too. That's a possibility. But it's also a possibility that the feedback loop most susceptable to failure won't affect the others much. It's possible that this will happen in a century. Or it's possible there are yet more feedback loops that we currently don't know about that'll push significant atomspheric temperature increase farther into the future.
What we do know is that there's definitely more energy in the atmosphere today. Weather events are getting more extreme. Stronger, more frequent storms. Colder cold snaps and hotter heat waves. And global temperatures are increasing, even if not by as much as predicted in the short term. Just keep in mind when thinking about these things that the entire planet isn't going to feel the same impact at the same time. It's about averages, over the entire system, over long periods of time (geological time scales). Also keep in mind that while certain one-off events can throw the numbers off, the trends will continue barring no behaviorial changes on our part.
The ultimate point is, we, if not as a species then as a civilization, are not facing any imminent danger yet, but we're getting more vulnurable, and by our own doing. It'd be nice to not be digging our own grave, no matter if we're using a large shovel or our bare hands. Of course, it all may not matter in the long run and our civilization and our species will ultimately be doomed anyway. But I'd rather not think that way.