Natural hazard models are vital for all phases of risk assessment and disaster management. However, the high number of uncertainties inherent to these models is highly challenging for crisis communication. The non-communication of these is problematic as interdependencies between them, especially for multi-model approaches and cascading hazards, can result in much larger deep uncertainties. The recent upsurge in research into uncertainty communication makes it important to identify key lessons, areas for future development, and areas for future research. We present a systematic thematic literature review to identify methods for effective communication of model uncertainty. Themes identified include a) the need for clear uncertainty typologies, b) the need for effective engagement with users to identify which uncertainties to focus on, c) managing ensembles, confidence, bias, consensus and dissensus, d) methods for communicating specific uncertainties (e.g., maps, graphs, and time), and e) the lack of evaluation of many approaches currently in use. Finally, we identify lessons and areas for future investigation, and propose a framework to manage the communication of model related uncertainty with decision-makers, by integrating typology components that help identify and prioritise uncertainties. We conclude that scientists must first understand decision-maker needs, and then concentrate efforts on evaluating and communicating the decision-relevant uncertainties. Developing a shared uncertainty management scheme with users facilitates the management of different epistemological perspectives, accommodates the different values that underpin model assumptions and the judgements they prompt, and increases uncertainty tolerance. This is vital, as uncertainties will only increase as our model (and event) complexities increase.