Software testing practices and processes in many companies are far from being mature and are usually conducted in ad-hoc fashions. Such immature practices lead to various negative outcomes, e.g., the ineffectiveness of testing practices in detecting all the defects, and cost and schedule overruns of testing activities. To conduct a test maturity assessment (TMA) and test process improvement (TPI) in a systematic manner, various TMA/TPI approaches and frameworks have been proposed. Motivated by a recent industrial project in TMA/TPI and to identify the state-of-the-art and the –practice in this area and to find out what we know about TMA/TPI, we conducted a multivocal literature review (a systematic review from various sources) on both the scientific literature and also practitioners grey literature (e.g., blog posts) and we present the results in this paper. By summarizing what we know about TMA/TPI, our review identified 58 different test maturity models and a large number of sources with varying degrees of empirical evidence on this topic. This article aims to benefit the readers (both practitioners and researchers) by serving as an evidence-based overview and index to the vast body of knowledge in this important and fast-growing area, in assessing and improving the maturity of test processes by benefitting from both the state-of-the-art and practice.