In this talk, which is meant to be an introduction to oo-categories, I will use Grothendieck's "Homotopy Hypothesis" as a narrative thread to motivate and give intuition for oo-categories. I will further try to briefly indicate how the practice of this theory actually works, and, in the end, explain how oo-categories provide a framework to revisit and refine the homotopy hypothesis. No prior knowledge of oo-categories will be assumed, though a vague idea of what they might be will be helpful.