Why it matters
Greedy is often the fastest algorithm when it works. Recognizing when it applies avoids over-engineering with DP or search.
The architecture
A greedy algorithm: at each step, choose the option that looks best locally, commit to it, don't reconsider.
Correctness proofs: exchange argument (show any solution can be transformed to greedy without loss), or optimal substructure (subproblem after greedy choice has same structure).
How it works end to end
Activity selection: sort by end time, greedily pick non-overlapping activities. Correct because earliest-end-time never hurts.
Huffman coding: greedily merge two lowest-frequency symbols. Produces optimal prefix code.
Dijkstra: always relax edges from the closest unvisited node. Correct with non-negative weights.
Interval scheduling and interval partitioning have variants with different greedy heuristics.