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Due to critical environmental and technological issues, there is a pressing need to switch from current refrigeration methods based on compression of gases to novel solid-state cooling technologies. Solid-state cooling is based on the thermal response of materials to external magnetic, electric, or mechanic fields, the so-called caloric effect. The electrocaloric (EC) effect, which is caused by electric fields and typically occurs in polar materials, is particularly promising from a technological point of view owing to its good scalability and natural implementation in circuitry. Simulation of EC effects represents an efficient and physically insightful strategy for advancing the field of solid-state cooling by complementing, and in some cases guiding, experiments. Theoretical estimation of EC effects can be achieved with different approaches ranging from computationally inexpensive but physically insightful phenomenological free-energy models to computationally very demanding and quantitatively accurate first-principles methods. In this Chapter, we review EC simulation approaches that rely on first-principles methods. In this category, we include ab initio quasi-harmonic methods, bond-valence and classical interatomic potentials and effective Hamiltonians. In analogy to the experiments, these simulation approaches can be used to estimate EC effects either directly or indirectly and we review here well-established protocols that can be followed for each case. The Chapter finalises with a collection of representative examples in which first-principles based approaches have been used to predict and understand original EC effects.