Trust in climate science provides the foundation for evidence-based policymaking on climate change mitigation and adaptation and public perceptions of the urgency of climate change. Here we consider the possibility that lack of public trust in climate science and climate scientists may undermine the effectiveness of climate science communication. To this end, we narratively review three topics of relevance to climate science and climate scientists. 1) The current state of trust; 2) Reasons for distrust; 3) How political engagement affects trust. We then draw on insights from communication and behavioral science to recommend how climate change communicators can become more trustworthy.