The concept of software testability has been researched in several different dimensions, however the relation of this important concept with other quality attributes is a grey area where existing evidence is scattered. The objective of this study is to present a state-of-the-art with respect to issues of importance concerning software testability and an important quality attribute: software robustness. The objective is achieved by conducting a systematic literature review (SLR) on the topic. Our results show that a variety of testability issues are in focus with observability and controllability issues being most researched. Fault tolerance, exception handling and handling external influence are prominent robustness issues in focus.