The fractional quantum Hall effect is a quintessential collective state of electrons, which has produced a plethora of remarkable new concepts.

I will begin with an introduction to composite fermions, topological bound states of electrons and quantized vortices, and illustrate how their emergence

provides a natural explanation for the prominent phenomenology of the fractional quantum Hall effect. I will then present a generalization, called the parton construction,

that captures certain other delicate fractional quantum Hall states. The talk is intended to be understandable to someone not familiar with this topic.