I actually had a quick stint at a reproductive laboratory on campus a while back, and this was always a question that people asked me. There is a reaction when the sperm meets the egg, the sperm has to break apart in order to get its DNA to mix with the egg’s DNA.
Curiously, the way fertility is presented, it’s often with the egg being a passive participant, but this couldn’t be further from the truth. Eggs have to make it from the ovaries to the uterus, then they interact in very complicated dynamics with the sperm. This is true in humans and all species with sexual reproduction.
I’m starting a collaboration with a group studying proto-sperm and portage in a fungus. What’s cool is that the sperm and egg are only slightly different shaped and both can move around pretty readily.