In this review, we describe both theoretical and experimental results on the dynamics of liquid bridges under isothermal conditions with fixed triple contact lines. These two major restrictions allow us to focus on a well-defined body of literature, which has not as yet been reviewed in a comprehensive way. Attention is mainly paid to liquid bridges suspended in air, although studies about the liquid-liquid configuration are also taken into account. We travel the path from equilibrium to nonlinear dynamics of both Newtonian liquid bridges and those made of complex fluids. Specifically, we consider equilibrium shapes and their stability, linear dynamics in free and forced oscillations under varied conditions, weakly nonlinear behavior leading to streaming flows, fully nonlinear motion arising during stretching and breakup of liquid bridges, and problems related to rheological effects and the presence of surfactant monolayers. Although attention is mainly paid to fundamental aspects of these problems, some applications derived from the results are also mentioned. In this way, we intend to connect the two approaches to the liquid bridge problem, something that both theoreticians and experimentalists may find interesting.