In our Solar System, there are numerous mean-motion resonances for the minor bodies and satellites, but there are no mean-motion resonances between the planets. The first mean-motion resonance in an extrasolar planetary system – the 2:1 resonance between two Jupiter-mass planets around the star GJ 876 – was discovered in 2001. Since then, an increasing number of pairs of planets in or near mean-motion resonances and resonant chains of three or more planets have been detected. I will discuss the dynamics of these systems and the constraints that they provide on the formation and dynamical evolution of planets. Topics will include high-order mean-motion resonances in the HD 202206 and nu Ophiuchi systems and the formation of resonant chains near the inner edge of protoplanetary disks.