Most trainers recommend using movements such as bodyweight squats and lunges at high repetitions.
According to some research published about a year ago, high rep training may actually build muscle! According to the research:
“Rather than grunting and straining to lift heavy weights, you can grab something much lighter but you have to lift it until you can’t lift it anymore,” says Stuart Phillips, associate professor of kinesiology at McMaster University. “We’re convinced that growing muscle means stimulating your muscle to make new muscle proteins, a process in the body that over time accumulates into bigger muscles.”
This would explain why bodyweight athletes such as gymnastics, dancers, parkour athletes, and those big guys that post videos of themselves doing crazy things on the monkey bars are so big and strong: repetition, repetition, repetition.
Even Arnold and other oldschool bodybuilders talked about high repetitions. However, these bodybuilders also challenged themselves with heavier weights. (I would also argue that what is heavy to us is light to them).
But the bottom line is that “going for the pump” works. It may not be as efficient as lifting heavy weights at low repetitions, but when you have no access to weights, than just cranking out dozens of bodyweight squats in your garage may be the way to go.