This paper provides an overview of quantum phase transitions in strongly-correlated electron systems. 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. They are characterized by quantum fluctuations in the ground state and are described by critical exponents related to energy and length scales. The paper discusses the derivation of an effective bosonic model for the fluctuations of ordering fields and the role of perturbative renormalization group (RG) and self-consistent renormalized spin fluctuation (SCR-SF) theories in understanding the quantum-classical crossover near the quantum critical point. It also highlights the importance of the upper-critical dimension $ D_C = 4 $, below which mean-field theory is no longer valid. The paper presents an alternative tricritical crossover approach valid at $ D < D_C $ in the large-N limit. It also discusses experimental studies of second-order quantum phase transitions, such as in $ LiHoF_4 $ and heavy-fermion compounds, and recent inelastic neutron scattering experiments that reveal unusual scaling laws in $ \omega/T $ for the dynamical spin susceptibility, indicating critical local modes beyond the itinerant magnetism picture. The paper concludes by emphasizing the need for new theories to describe local quantum critical points in itinerant systems.This paper provides an overview of quantum phase transitions in strongly-correlated electron systems. 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. They are characterized by quantum fluctuations in the ground state and are described by critical exponents related to energy and length scales. The paper discusses the derivation of an effective bosonic model for the fluctuations of ordering fields and the role of perturbative renormalization group (RG) and self-consistent renormalized spin fluctuation (SCR-SF) theories in understanding the quantum-classical crossover near the quantum critical point. It also highlights the importance of the upper-critical dimension $ D_C = 4 $, below which mean-field theory is no longer valid. The paper presents an alternative tricritical crossover approach valid at $ D < D_C $ in the large-N limit. It also discusses experimental studies of second-order quantum phase transitions, such as in $ LiHoF_4 $ and heavy-fermion compounds, and recent inelastic neutron scattering experiments that reveal unusual scaling laws in $ \omega/T $ for the dynamical spin susceptibility, indicating critical local modes beyond the itinerant magnetism picture. The paper concludes by emphasizing the need for new theories to describe local quantum critical points in itinerant systems.