This chapter discusses the notions of state of matter and phase of matter. It looks at two categories of ‘anomalous behaviours’ in thermodynamics: pressure plateaus in the isotherms of real gases, and the appearance of a magnetic state in ferromagnet. The former situation lends itself to a thermodynamic analysis with the van der Waals equation of state. A full analysis is proposed and the interpretation of the pressure plateau as stemming from the coexistence between two different phases at different densities is identified. Various laws, such as the latent heat law and Clapeyron’s law, are derived as well from thermodynamic theory. In the case of magnetism, there is no equation of state that would play a role analogous to the van der Waals equation of state. Statistical mechanics is required to understand the physics at play in the system. This is done by looking at the paradigmatic Ising model. The mean-field approach to this model is proposed and the existence of a ferromagnetic phase, breaking the underlying symmetry of the system, is observed.