Context: Software testability is the degree to which a software system or a unit under test supports its own testing. To predict and improve software testability, a large number of techniques and metrics have been proposed by both practitioners and researchers in the last several decades. Reviewing and getting an overview of the entire state-of-the-art and state-of-the-practice in this area is often challenging for a practitioner or a new researcher. Objective: Our objective is to summarize the body of knowledge in this area and to benefit the readers (both practitioners and researchers) in preparing, measuring and improving software testability. Method: To address the above need, the authors conducted a survey in the form of a systematic literature mapping (classification) to find out what we as a community know about this topic. After compiling an initial pool of 303 papers, and applying a set of inclusion/exclusion criteria, our final pool included 208 papers (published between 1982 and 2017). Results: The area of software testability has been comprehensively studied by researchers and practitioners. Approaches for measurement of testability and improvement of testability are the most-frequently addressed in the papers. The two most often mentioned factors affecting testability are observability and controllability. Common ways to improve testability are testability transformation, improving observability, adding assertions, and improving controllability.Conclusion: This paper serves for both researchers and practitioners as an "index" to the vast body of knowledge in the area of testability. The results could help practitioners measure and improve software testability in their projects. To assess potential benefits of this review paper, we shared its draft version with two of our industrial collaborators. They stated that they found the review useful and beneficial in their testing activities. Our results can also benefit researchers in observing the trends in this area and identify the topics that require further investigation.