Purpose of Review The deployment of hardware (e.g., robots, satellites, etc.) to space is a costly and complex endeavor. It is of extreme importance that on-board systems are verified and validated through a variety of verification and validation techniques, especially in the case of autonomous systems. In this paper, we discuss a number of approaches from the literature that are relevant or directly applied to the verification and validation of systems in space, with an emphasis on autonomy. Recent Findings Despite advances in individual verification and validation techniques, there is still a lack of approaches that aim to combine different forms of verification in order to obtain system-wide verification of modular autonomous systems. Summary This systematic review of the literature includes the current advances in the latest approaches using formal methods for static verification (model checking and theorem proving) and runtime verification, the progress achieved so far in the verification of machine learning, an overview of the landscape in software testing, and the importance of performing compositional verification in modular systems. In particular, we focus on reporting the use of these techniques for the verification and validation of systems in space with an emphasis on autonomy, as well as more general techniques (such as in the aeronautical domain) that have been shown to have potential value in the verification and validation of autonomous systems in space.