The subject of consideration is the pseudospin‐electron model (PEM) which appears in the description of locally anharmonic crystalline and molecular systems with strong electron correlations. A review of the main results concerning thermodynamics, energy spectrum and dynamics of the model is given. Thermodynamically stable states and phase transitions in the system are investigated in the regimes of constant chemical potential or the fixed electron concentration both within the framework of the generalized random phase approximation and the dynamical mean field scheme. A comparison is performed with thermodynamics of the Falicov‐Kimball model. An attention is called to the possibility of applying of the PEM to the description of high‐Tcsuperconductors as well as to the H‐bonded systems with the transition metal ions. © 2003 American Institute of Physics