The BiOeconomic mArine Trophic Size-spectrum (BOATS) model is a sophisticated digital tool designed to simulate the global fishery as a dynamic, coupled ecological-economic system. Its primary use case in research and lab work involves predicting the growth and reproduction of multiple fish size spectra across global grid cells. This is achieved by integrating local water temperature and net primary production data, which can be sourced from observational datasets or coupled biogeochemical-climate models. Technically, BOATS is developed in MATLAB, with version 1.0 available for download, and BOATSv2 being the most recently finalized iteration. The model predicts the intensity of fishing effort in each grid cell over time, responding to economic profit determined by factors such as catchability, fish price, fishing cost, and catchable biomass. Key capabilities of BOATSv2 include advanced features like dynamic fisheries management and the ability to separate demersal and pelagic fish populations, providing a significantly improved simulation of high seas fisheries that aligns well with observations. The model operates on a 1°x1° grid with a monthly mean timestep, and for Fish-MIP simulations, it considers three size groups (small, medium, large) representing commercial fish. BOATS is widely applied in various research areas, contributing regularly to the Fisheries and Marine Ecosystems Model Intercomparison Project (Fish-MIP) ensemble. It has been instrumental in estimating global biomass and biogeochemical cycling of marine fish, both with and without fishing impacts. The model has also been used to analyze the response of global fisheries to sudden climatic shocks, such as those simulated after a nuclear war, and to study the importance of regulation strength and technology creep in long-term fisheries projections. Furthermore, BOATS simulations decompose the effects of climate change into temperature and primary production components, illustrating their spatial variation and interaction with fishing pressure. It has provided mechanistic insights into the historical progression of industrial fisheries, showing how bioenergetics favored early development in cold water ecosystems. Additional features of the BOATS model include its contribution to multi-model ensembles like Fish-MIP, which helps in understanding trophic amplification of ocean biomass declines with climate change. The model's ability to simulate how fish catches respond to dynamic fishing effort allows for optimization of ecological parameters against observational reconstructions of fish catches. It has also provided new estimates of global fish biomass and cycling rates, highlighting the impact of fishing on carbon sequestration and biogeochemical cycles. The model's framework allows for the integration of various climate model simulations and observational data, making it a versatile tool for assessing complex interactions within marine ecosystems.