In this chapter, we survey methods that perform keyword search on graph data. Keyword search provides a simple but user-friendly interface to retrieve information from complicated data structures. Since many real life datasets are represented by trees and graphs, keyword search has become an attractive mechanism for data of a variety of types. In this survey, we discuss methods of keyword search on schema graphs, which are abstract representation for XML data and relational data, and methods of keyword search on schema-free graphs. In our discussion, we focus on three major challenges of keyword search on graphs. First, what is the semantics of keyword search on graphs, or, what qualifies as an answer to a keyword search; second, what constitutes a good answer, or, how to rank the answers; third, how to perform keyword search efficiently. We also discuss some unresolved challenges and propose some new research directions on this topic.