Throughout its lifetime, software must be changed for many reasons, such as bug fixing, performance tuning, and code restructuring. Testing modified software is the main activity performed to gain confidence that changes behave as they are intended and do not have adverse effects on the rest of the software. A fundamental problem of testing evolving software is determining whether test suites adequately exercise changes and, if not, providing suitable guidance for generating new test inputs that target the modified behavior. Existing techniques evaluate the adequacy of test suites based only on control- and data-flow testing criteria. They do not consider the effects of changes on program states and, thus, are not sufficiently strict to guarantee that the modified behavior is exercised. Also, because of the lack of this guarantee, these techniques can provide only limited guidance for generating new test inputs. This research has developed techniques that will assist testers in testing evolving software and provide confidence in the quality of modified versions. In particular, this research has developed a technique to identify testing requirements that ensure that the test cases satisfying them will result in different program states at preselected parts of the software. This research has also developed supporting techniques for identifying testing requirements. Such techniques include (1) a differencing technique, which computes differences and correspondences between two software versions and (2) two dynamic-impact-analysis techniques, which identify parts of software that are likely affected by changes with respect to a set of executions.