Karp's 21 NP-complete problems are a set of computational problems that are significant in the field of computer science, particularly in theory of NP-completeness. Introduced by Richard Karp in 1972, these problems are known for their difficulty, as no efficient algorithm has been found to solve them in all cases. They serve as benchmarks for understanding the limits of what can be computed quickly. These problems include well-known examples such as the Traveling Salesman Problem, the Knapsack Problem, and Graph Coloring. Each problem has unique characteristics but shares the common trait of being solvable in polynomial time if a solution is provided, making them crucial for studying algorithm efficiency and complexity.