With the ever-increasing number of artificial intelligence (AI) systems, mitigating risks associated with their use has become one of the most urgent scientific and societal issues. To this end, the European Union passed the EU AI Act, proposing solution strategies that can be summarized under the umbrella term trustworthiness. In anti-cancer drug sensitivity prediction, machine learning (ML) methods are developed for application in medical decision support systems, which require an extraordinary level of trustworthiness. This review offers an overview of the ML landscape of methods for anti-cancer drug sensitivity prediction, including a brief introduction to the four major ML realms (supervised, unsupervised, semi-supervised, and reinforcement learning). In particular, we address the question to what extent trustworthiness-related properties, more specifically, interpretability and reliability, have been incorporated into anti-cancer drug sensitivity prediction methods over the previous decade. In total, we analyzed 36 papers with approaches for anti-cancer drug sensitivity prediction. Our results indicate that the need for reliability has hardly been addressed so far. Interpretability, on the other hand, has often been considered for model development. However, the concept is rather used intuitively, lacking clear definitions. Thus, we propose an easily extensible taxonomy for interpretability, unifying all prevalent connotations explicitly or implicitly used within the field.