We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter g like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent z related to the energy and length scales Δ and ξ. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension D_C=4 (where

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... z and d is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in ω /T for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.