This survey introduces contract design to computer scientists: using outcome-based payments to incentivize effort. We discuss applications that motivate a computational approach to contract design, ranging from online labor markets, to incentive-aware algorithmic classification, to emerging ecosystems of AI agents. We present the classic principal-agent model and introduce basic concepts. We show how optimal contracts are computable via linear programming, and why they can be opaque and brittle. Motivated by this we turn to simpler contract formats, specifically linear contracts. We discuss approximation guarantees, and robust (max-min) optimality of such contracts. We then move beyond the single-agent setting to combinatorial contract settings with multiple agents, mapping the algorithmic landscape of tractability and approximation. Finally, we discuss partial information settings through the lens of learning algorithms, and outline open directions. The goal is a concise, accessible entry point that connects economic foundations with algorithmic tools and highlights opportunities for new theory and applications.

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