MegaSaM is a system that allows for accurate, rapid, and robust estimation of camera parameters and depth maps from monocular videos of dynamic scenes. This system overcomes the limitations of traditional structure-from-motion and monocular SLAM techniques, which typically assume that the input videos primarily contain static scenes with significant parallax. MegaSaM can be extended to videos of complex dynamic scenes in the real world, including those with unknown fields of view and unconstrained camera paths, through carefully modified depth-visual SLAM frameworks. Extensive experiments on both synthetic and real videos demonstrate that MegaSaM is more accurate and robust in camera pose and depth estimation while being faster or comparable in runtime to previous and concurrent work.