Earth System models (ESMs) remain our best tool for process-level understanding of climate. Unfortunately, such models are computationally expensive to run and require millions of person-hours to develop. Therefore, flexible reduced-complexity models have been created to efficiently emulate the large-scale behavior ESMs in a fraction of the time. Key Earth System processes such as the carbon cycle, atmospheric chemistry, and the climate response to forcing are parameterised using simple functional relationships that are based on our knowledge of the underlying physics or the behavior of ESMs. To ensure reliability of reduced-complexity models, a two step process is performed: calibration and constraint. Calibration involves tuning the emulator response to reproduce the global mean responses of existing ESMs, by appropriate selection of model parameters. This calibration provides the basis for a joint probability distribution of parameter sets from which a large Monte Carlo ensemble can be generated. The Monte Carlo ensemble is run in the emulator, and then the constraint step rejects parameter combinations that generate simulated climates that are not in agreement with historical observed climate change and assessments of the distribution of key climate variables (e.g. the equilibrium climate sensitivity from the IPCC). This results in a smaller posterior ensemble that can be used for making reliable climate projections whilst preserving observational and assessed uncertainty in our knowledge of the climate system. In this talk I will demonstrate many of these processes using the FaIR model (v2.1) as an example. Applications of reduced-complexity models include policy-relevant climate projections and coupling to economic models of climate change. The Working Group 3 contribution to the IPCC Sixth Assessment Report assessed nearly 2000 emissions scenarios with a turnaround time of three weeks in fall 2021; work that would be impossible with ESMs. In economic contexts (e.g. cost-benefit integrated assessment models), a joint state-space optimisation of climate and economic variables is performed, so the climate model needs to be iterated hundreds or thousands of times per scenario. Again, using a full-complexity model for this task is intractable. Reduced complexity models are currently being developed to emulate regional climate, extremes, tipping points, and poorly modeled components of the climate system.