The formulation of material models is both an art and a science, as it requires extensive knowledge and skillful tuning by the practitioner for every new material model. Machine learning techniques offer an automatized pipeline to this potentially tedious process but must be designed appropriately to deliver reliable results. This chapter considers both data-driven and physics-aware/physics-augmented approaches. It starts with elastic materials in one dimension, explains how neural networks can model linear and hyperelastic behavior, and how incorporating physical laws improves predictions drastically. Extensions to viscoelastic materials explore architectures like recurrent neural networks and thermodynamic consistency constraints. For three-dimensional solids, advanced techniques such as invariant-based and deformation gradient-based physics-augmented neural networks are introduced. The chapter provides practical examples to convey these methods didactically and highlights their potential to transform current material modeling by integrating learning (from data) techniques with established physical principles.