What's with the new wheel and tire sizes these days?

I’ve noticed that car rims are getting larger and larger, and the tires are getting thinner and thinner. Sorry, there must be a better word than “thinner”, but I couldn’t come up with one. I mean that there seems to be less and less “rubber” on the tires because the rim diameter seems to be getting larger. This is true even of passenger cars. Why is that?
Is this for better performance (like, on curves), better gas mileage, better control, or what?
Aren’t these tires (as well as the rims!) more susceptible to damage from potholes, and isn’t the ride less comfortable?