The regularity of the community size-spectrum, i.e., the fact that the total ecosystem biomass contained in logarithmically equal body size intervals remains constant, is a striking characteristic of marine ecosystems. Community size-spectrum models exploit this feature to represent marine ecosystems with two measures: the slope and the intercept (height) of the community spectrum. Size-spectrum models have gain popularity over time to model the properties of fish communities, whether to investigate the impact of fishing, or embedded into end-to-end models to investigate the impact of climate. We review the main features and state of the art developments in the domain of continuous size-spectrum models. The community spectrum emerges from a balance between size-selective predation, growth and biomass dissipation. Further to these basic components, reproduction and various causes of mortality have been introduced in recent studies to increase the model's realism or simply close the mass budget of the spectrum. These different processes affect the stability of the spectrum and affect the predictions of the size-spectrum models. A few models have also introduced a representation of life-history traits in the community size-spectrum. This allows accounting for the diversity of energy pathways in food webs and for the fact that metabolism is both size- and species-specific. The community-level metabolism therefore depends on the species composition of the community. The size-spectrum's regularity at the community level can serve as a conceptual basis for building theories of marine ecosystems’ functioning. It is also used as indicator of anthropogenic and natural disturbances. The mechanistic nature of size-spectrum models as well as their simple and aggregated representation of complex systems makes them good candidates as a strategic management tool. For instance, for testing the impact of different fishing management actions or for projecting marine ecosystem's states under various climate change scenarios.