Darwin's Radio by Greg Bear.
The very first chapter had Mitch, an anthropologist, mountain climbing to an intact Neanderthal family. I've read three or four novellas that were about mountain climbing and I had to slog and slog to get through them. Fortunately that part was over and done with quickly, and I was able to enjoy the rest of the novel.
The setting is our contemporary world, with the exception that a retrovirus has awoken and started to cause, well, that's what the scientists in the story are trying to figure out. Kaye Lang is a molecular biologist, who had a paper describing HERV. Which turns out to be significant, in that an active form of the virus, named SHEVA, starts causing Herod's disease. That main fallout of this is a lot of miscarriages.
The action follows Kaye, the Center for Disease Control and other government health agencies, and a little bit with Mitch, who found those neanderthal mummies that exhibit some of the same characteristics that seem to be going on now with us. Is SHEVA a disease or a mechanism for an evolutionary jump? The premise is kinda cool -- that the basis for an evolutionary jump could already be within our DNA -- and the story following Kaye, Christopher, Mitch, Augustine, etc. was very very good.
I kind of hesitate to refer to the book as a classic, but if it's not, it's close. I had to look up the 2000 Hugos. I see that Darwin's Radio is nominated. I can't argue with A Deepness in the Sky having won, that's another great novel.