Actually, we do understand a lot of the neural 'mechanics' that drive emotion in the brain. We even understand why it had to evolve that way.
While still trying to retain some semblance of brevity, a human brain is made up of 3 systems, all operating simultaneously and that have specific purposes. The Cerebellum is the (hard-wired electrical) system that drives the muscles (including the heart) and primary instincts, like hunger, survival, procreation, etc. Emotions are driven by the (chemical) Limbic system, or reptilian brain. This evolved because pure instinct can get you into trouble when things like hunger and survival are in conflict. Whereas fear gives context to that situation, and allows for a statistically higher chance of survival.
Finally, you have the (soft-wired electrical) Cerebral Cortex, or mammalian brain. This is the seat of reason, and is 'programmable' so that the organism can modify its behaviour according to environment, meaning that survival is now possible even in environments that change faster than evolution can keep up.
Classical computers have the equivalent of a cerebellum (BIOS etc.) and a cerebral cortex (OS and Applications), but it doesn't have a system for chemical disruptions per se.
These chemical disruptions can be simulated, but they cannot be experienced by computers. So, in that sense, computers can never 'feel' emotions in the same way that we do.
A broader point that's related to this is that even if a computer ever achieves sentience as we understand it, it won't be human. We may be able to simulate a sense of survival, hunger, etc. but that's a really bad idea for many reasons outside the scope of this question and even if we did do it, the simulation may make such an intelligence 'feel' human to us, but that's a result of our own anthropomorphisation of the AI; we would be inferring intelligence upon the AI, it would not be implying it to us.
Even the term 'artificial intelligence' should imply that we are talking about the ability to simulate a general processing capability, which is very different to the question of sentience. That the only sentient entities we've ever observed are living humans, it doesn't follow that a computer that is intelligent is either sentient or living. This is a simple classification error because classification only goes in one direction; object to group. You can classify all bees as insects, but you can't classify all insects as bees.
In like manner, all living humans are intelligent, but not all possible intelligences will be alive or think like humans.
