In many companies, software testing practices and processes are far from mature and are usually conducted in an ad hoc fashion. Such immature practices lead to negative outcomes - for example, testing that doesn't detect all the defects or that incurs cost and schedule overruns. To conduct test maturity assessment (TMA) and test process improvement (TPI) systematically, researchers and practitioners have proposed various approaches and frameworks. Motivated by a recent industrial project in TMA and TPI and wanting to identify the state of the art and practice in this area, researchers conducted a review of both the scientific literature and practitioners' gray literature (for example, blog posts). The review identified 58 test maturity models and many sources with varying degrees of empirical evidence. The review's results can serve as an evidence-based overview of and index to the vast body of knowledge in this important, fast-growing area. Using this knowledge, both researchers and practitioners should be able to assess and improve the maturity of test processes.