To me the "coolest" feature is that it saves dormant copies in cells, so that even if there is no detectable virus in the blood, a few months after stopping taking anti-HIV drugs the virus will reappear. If you sample the virus right when the first spike reappears, you will see a bunch of different HIV virus types, essentially the history of each mutation on that person, as each virus strain saves its own copies... (soon after the strongest strain dominates)

If you want a more-than-surface-deep (but not academic deep) article on what makes HIV fascinating - https://www.avert.org/professionals/hiv-science/overview is a good quick read

A person with HIV will actually be infected by multiple variants simultaneously, since the virus mutates rapidly within a single host (tons of variants will be produced in a single day). So, even though the immune system will fight the virus and produce antibodies, the virus stays one step ahead. That also means that a person will not develop long-term immunity after being exposed to the live virus (and can even be infected multiple times with different variants and strains), and is the main challenge with developing an HIV vaccine.

I am no expert but my understanding is that AIDS occurs when a variant targeting receptors more specific to CD4 T-cells begins replicating (or begins replicating at too high a rate), which results in T-cell counts falling below some threshold. So a person will go through an extended period without feeling any symptoms, possibly transmitting the virus to others (hence the importance of widespread, easy access to testing), only to be incapacitated by AIDS later when the "balance" of the variants changes (assuming they do not receive HIV-suppressing medications).