This chapter provides an extensive review of the analytical solutions that have been developed for problems on phase change in PCMs. Analytical modelling provides valuable insights into the fundamental thermal behaviour of PCMs. It is also a computationally inexpensive alternative to numerical simulations. The chapter on the theoretical basis for these models addresses classical and recent solution techniques adopted to deal with composite systems, and finned configurations, as well as stand-alone lattice heat storage units under boundary conditions. It examines the main assumptions, thermophysical properties, and dimensionless parameters affecting phase change phenomena. Analytical, numerical, and experimental results are compared to illustrate the validity, effectiveness, and limitations of analytical techniques. The review illustrates how models of this kind can be used for the prediction of temperature profiles, phase front ablation rates, and general trends in thermal behaviour. The chapter concludes by discussing the research directions, including natural convection, non-ideal phase-transition model, and anisotropy. It proposes the integration of analysis methods and machine learning to address these problems.