Can you grow fruit if you don't have, say, a yard? Like, can you grow fruits inside your home? In a pot? Or something?

Cuz these strawberries I got from the supermarket are not only HUGE to the point of scary, but are hella bitter and rotting after like 3 days of having them. Hmph. Piffle.

So I want to grow my own fruit. I'm pretty decent at gardening when it comes to flowers, but I've never grown fruit before. Is it even possible to pull that off inside an apartment? I live in Brooklyn so the only "land" I have is my landlord's concrete driveway.