He is most notable for his research in the theory of algorithms, for which he received a Turing Award in 1985, The Benjamin Franklin Medal in Computer and Cognitive Science in 2004, and the Kyoto Prize in 2008.

[2] Karp was elected a member of the National Academy of Engineering (1992) for major contributions to the theory and application of NP-completeness, constructing efficient combinatorial algorithms, and applying probabilistic methods in computer science.

From 1988 to 1995 and 1999 to the present he has also been a research scientist at the International Computer Science Institute in Berkeley, where he currently leads the Algorithms Group.

[8] In 2012, Karp became the founding director of the Simons Institute for the Theory of Computing at the University of California, Berkeley.

[10] In 1973 he and John Hopcroft published the Hopcroft–Karp algorithm, the fastest known method for finding maximum cardinality matchings in bipartite graphs.