Model transformations are the key technique in Model-Driven Engineering (MDE) to manipulate and construct models. As a consequence, the correctness of software systems built with MDE approaches relies mainly on the correctness of model transformations, and thus, detecting and locating bugs in model transformations have been popular research topics in recent years. This surge of work has led to a vast literature on model transformation testing and debugging, which makes it challenging to gain a comprehensive view of the current state of the art. This is an obstacle for newcomers to this topic and MDE practitioners to apply these approaches. This paper presents a survey on testing and debugging model transformations based on the analysis of 140 papers on the topics. We explore the trends, advances, and evolution over the years, bringing together previously disparate streams of work and providing a comprehensive view of these thriving areas. In addition, we present a conceptual framework to understand and categorise the different proposals. Finally, we identify several open research challenges and propose specific action points for the model transformation community.