Data-driven computational mechanics offers an innovative solution methodology by replacing constitutive models with data spaces defining admissible material states. Originally proposed for linear elasticity, its application to plasticity remains challenging. Purely data-driven plasticity schemes are usually restricted to 1D problems due to the required excessively large data space resulting from path dependence. Hybrid frameworks combining constitutive assumptions with data have shown promise but are often limited by their underlying assumptions such as isotropic hardening or their inability to capture strain path changes. First, a new hybrid model–data plasticity framework is proposed that incorporates kinematic and isotropic hardening via data spaces derived from discrete datasets, while adopting Prager’s law for back stress evolution without explicitly defining its functional form. The proposed framework is based on von Mises plasticity, where the return-mapping equation is reduced to a single scalar equation, with the incremental change in effective plastic strain as the unknown. The isotropic and kinematic hardening are separately defined through the data only. The framework builds on the likelihood of representing the actual hardening behaviour in the data space. The construction of the data space as a data density field, consisting of a sum of Gaussian kernels, ensures that the return-mapping operator is reduced to a linear problem. Moreover, if the constructed data space is a monotonic increasing function of the effective plastic strain, thermodynamical consistency is satisfied a priori. The approach preserves the standard computational plasticity algorithmic procedures, while an implicit return-mapping procedure and a search direction calculation akin to the elasto-plastic tangent are performed through the data spaces. Numerical examples in 1D/3D problems demonstrate the effectiveness of the proposed framework. Next, a hybrid approach is presented for anisotropic plasticity, whereby no explicit form of the global yield function is adopted. Relying on a typical experimental anisotropic dataset, a local data-informed yield surface patch is defined. The hybrid solution algorithm is constructed on that basis, and demonstrated for a number of 3D problems under complex loading conditions. To assess the performance, comparisons are made with a fully model based solution, from which a virtual dataset was extracted first.