The mechanical properties of metallic materials result from their microstructure. The superior properties of advanced high-strength steels (AHSS) compared to conventional single-phase steels are the result of a much more complex microstructure that firstly contains multiple phases and secondly has a staggered internal hierarchy (bainitic steels, martensitic steels) and thirdly can offer different deformation mechanisms (TRIP steels, TWIP steels). Therefore, to understand the behaviour of existing AHSS grades and to develop new alloying concepts for grades with improved properties, it is essential to understand the mechanical behaviour of both the individual microstructural components and their joint interaction. Full-field simulation techniques that solve for mechanical equilibrium on a discretised microstructural model allow the study of collective behaviour as a function of constitutive models for elasticity, plasticity and damage of the individual constituents. In this way, simulations provide the opportunity to systematically investigate the influence of parameters such as strain hardening rate, crystallographic orientation and grain morphology. The numerical solvers typically used for full-field micromechanical simulations are based on the finite element method (FEM). This approach allows the discretisation of arbitrarily shaped bodies. Grain and subgrain-resolved microstructure models for AHSS can be based directly on experimentally characterised microstructures. With the availability of electron backscatter diffraction (EBSD), it became possible to measure not only the phase distribution but also the crystallographic orientation. The information obtained from micromechanical simulations can complement experimental results by providing stress state information not readily available from measurements or be used to investigate the influence of the mechanical properties of the individual constituents. Due to the complexity of AHSS microstructures, simulation approaches that explicitly consider all relevant microstructural details are the only modelling approaches that have sufficient predictive power to simulate properties. This results in one major scientific challenges: On the computational side, fast and robust numerical algorithms and physics-based constitutive models need to be developed that are appropriate for the material in question and capable of handling complex microstructures in full 3D.