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The continuum slip theory of crystals provides a canonical framework of finite plasticity with physically well‐defined roots in the dislocation mechanics of metals. Reliable algorithmic settings of crystal plasticity are not only needed for structural analyses of single crystals but also provide a cornerstone for multiscale computations of evolving anisotropic microstructures in metallic polycrystals. This article summarizes a current status of computational crystal plasticity and its application to the texture analysis of polycrystals. It outlines a basic constitutive structure of crystal plasticity, alternative deformation‐driven stress update algorithms and a computational scheme for the nonlinear homogenization of polycrystalline aggregates. Particular emphasis is put on a canonical incremental variational formulation for Schmid‐type crystal plasticity with potential hardening where an incremental stress potential is obtained from a local minimization problem with respect to the internal variables. The existence of this stress potential allows the formulation of IBVPs for elastic–plastic crystals as a sequence of incremental minimization problems. Furthermore, the nonlinear homogenization of polycrystalline microstructures may be recast into a principle of minimum averaged incremental energy. Within this variational setting of homogenization, a quasi‐hyperelastic incremental macro‐stress potential is obtained from a global minimization problem with respect to the fine‐scale displacement fluctuation field. The performance of the formulations is demonstrated for benchmarks of single crystal plasticity and texture developments in polycrystals.