Keep in mind that essentially all energy in the world comes, directly or indirectly, from sunlight. While caves may have some life most of it either regularly travels above ground for nourishment or hunts those that do. If the earth above was rendered inhospitable to all creatures the real issues would be starvation due to an inability to get food/energy.
The only two sources of energy, and thus food, that would be viable are geothermic, which is very limited, and sunlight. This means figuring out a way to grow/capture/use food from above ground to sustain the below population. Perhaps plants still grow reliably above ground and those living below can manage limited trips to fetch it? Still, if they are not farming that means far less food available, and thus a much smaller population, in any given area.
This is a follow up to the below comment, but is a point I feel deserves better stressed then my comment could, as I think it's the most important detail. Humanity's evolution, regardless of environment, is first and foremost driven by our technology! We no longer adapt to our environment, we adapt it to us. This doesn't mean we are not evolving, but it's a very different evolution then the type you're used to. We are evolving to be more intelligent, to better work in a complicated social enviroment where working with others is the only way to achieve anything, and evolving to work with our technology. We are not, however, evolving to be better suited to living in the cold, or heat, or any enviroment really because we simply build technology to work around our limitations.
For instance, our leading cause of death in America is heart disease. We would be evolving to not die from the fatty foods we eat. Our next most common cause of death is Cancer, which likely means slowly evolving means to detect and destroy cancerous cells (which our body already does a pretty good job of, only a very very tiny fraction of cancerous cells become cancer). Of course, those are today's causes of death, with as fast as our technology evolves, our leading cause of death in 2 generations may be completely different; which means we won't really have time to evolve to adapt to those particular threats. Instead the long term adaptions will likely all be about working in social groups, use of technology, and general fertility.
This makes questions of human evolution in the underground hard to answer, since first I have to ask what technological approach we would use to adapt the underground. For instance our eyes are a great example. Plenty of cave-dwelling species have either lost their eyes or had then degrade to a fraction of what they were, since being able to detect light is useless in an enviroment where there is no light and eyes are a vulnerable spot we need to protect. Does that mean our eyes would degrade, probably not! Humans would instead set up lights to allow them to see like the did above ground, because that's how we work now and it's allot easier to adapt our enviroment to support our need for light then it is to adapt our eyes to work without light. Over a few generations we may get better about seeing in darker areas perhaps, but our eyesight would not be significantly changed unless we were unable to create lights. The same principle exists everywhere, we will adapt our enviroment to our current needs long before we would evolve to better suit our enviroment!
Some changes may still occur in terms of physical evolution over a short time period, However, these will be simply favoring certain existing genomes over others. Certain types of humans may become more common rapidly, for instance perhaps one skin tone is less prone to vitamin deficency from lack of light then others, or maybe short people may quickly become dominant as it becomes hard to survive in tunnels if you're too tall. These changes could start to have a measurable, though still not overwhelming, effect in a small number of generations if a substantial enough number of humans die out (the more deaths, the more evolutionary pressure) However, this isn't creating new phenotypes, simply prioritizing certain existing ones. Humans would still look human, just with certain types of humans being a bit more/less common. It would take a huge number of generations to have any significant change to phenotype, for humans to start looking different than humans of today. By that time, our technology and culture should have adapted to the difficulties of living underground and we would have long since adapted our enviroment to support us. In short, I don't anticipate any huge change in human structure or format, at most, certain current physical traits become more common. Which become more common, depends on what evolutionary pressures we were unable to address with our technology. IF I knew exactly what enviroment humans would create for themselves below ground, I could anticipate what the most common things to kill us below ground were and anticipate what evolutionary pressures they would give us. However, I would first need to project our technological and cultural adaptations before I could begin to infer our evolutionary ones.
The end result is that I see this question as being one about how our technology and culture will evolve and adapt. The real question is what cool technology will we use to work around whatever problems forced us underground. That technology drives everything else, and is a very interesting question in it's own right. However, it's also a very difficult question to answer without knowing very exact details as the cause of our moving underground, thus the reason I have to ask follow up questions to give any useful advice.
Since sunlight is such a huge source of energy for...everything humanity would therefore do everything they could to find a way to harness that energy. Thus exactly how off-limits the above world is would be a huge question, because we will find a way to use technology to harness the energy and light above ground if at all possible, and that ability impacts everything about later technological, cultural, and physical evolution.
The question of how much warning humanity has before being forced below ground is also critical. How much technology we have to help us adapt depends on how much time we had to develop and build technology before moving below ground, which in turn affects everything about eventual development.
Finally how many humans died during the first 1-2 generations is a huge factor on whether we would notice any phenotype difference due to moving underground. If only 10-20% of humanity died out, then I wouldn't expect a huge difference in phenotype, beyond skin coloration, to occur because we clearly adapted our enviroment fast enough to avoid facing significant evolutionary pressures. if 50% of the population died out, then we would expect to see those with existing phenotypes that are better adapted to life below ground to be the norm. Again this is more about how common or perhaps exaggerated existing traits are, they would still likely look mostly human.