This chapter provides an introduction to quantum phase transitions in strongly-correlated electron systems, focusing on second-order transitions. These transitions occur at zero temperature when a non-thermal parameter, such as pressure, chemical composition, or magnetic field, is tuned to a critical value. The transitions are characterized by dynamic exponents and scales related to energy and correlation lengths. The chapter discusses the derivation of an effective bosonic model for the fluctuations of ordering fields, the determination of an upper-critical dimension, and the application of perturbative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover near the quantum critical point. It also highlights recent inelastic neutron scattering experiments on heavy-fermion systems that reveal critical local modes beyond the itinerant magnetism picture. The chapter concludes by mentioning new attempts to describe this local quantum critical point, including dynamical mean-field theory and supersymmetric approaches.This chapter provides an introduction to quantum phase transitions in strongly-correlated electron systems, focusing on second-order transitions. These transitions occur at zero temperature when a non-thermal parameter, such as pressure, chemical composition, or magnetic field, is tuned to a critical value. The transitions are characterized by dynamic exponents and scales related to energy and correlation lengths. The chapter discusses the derivation of an effective bosonic model for the fluctuations of ordering fields, the determination of an upper-critical dimension, and the application of perturbative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover near the quantum critical point. It also highlights recent inelastic neutron scattering experiments on heavy-fermion systems that reveal critical local modes beyond the itinerant magnetism picture. The chapter concludes by mentioning new attempts to describe this local quantum critical point, including dynamical mean-field theory and supersymmetric approaches.