The study of ecosystems, both natural and artificial, has historically been mediated by population dynamics theories. In this framework, quantifying population numbers and related variables (associated with metabolism or biological-environmental interactions) plays a central role in measuring and predicting system-level properties. As we move towards advanced technological engineering of cells and organisms, the possibility of bioengineering ecosystems (from the gut microbiome to wildlands) opens several questions that will require quantitative models to find answers. Here, we present a comprehensive survey of quantitative modelling approaches for managing three kinds of synthetic ecosystems, sharing the presence of engineered strains. These include test tube examples of ecosystems hosting a relatively low number of interacting species, mesoscale closed ecosystems (or ecospheres), and macro-scale, engineered ecosystems. The potential outcomes of synthetic ecosystem designs and their limits will be relevant to different disciplines, including biomedical engineering, astrobiology, space exploration and fighting climate change impacts on endangered ecosystems. We propose a space of possible ecosystems that captures this broad range of scenarios and a tentative road map for open problems and further exploration.