Active motion is a ubiquitous phenomenon in nature. It can be found across many length scales, from nanoscopic motor proteins traveling along microtubule highways within cells, over microscopic cells themselves actively moving in search for nutrients, up to macroscopic animals. From a physical point of view, the particles in these systems share the ability to steadily convert energy from an internal or external source into mechanical work. Therefore, they force the system out of equilibrium. Any natural organism in equilibrium would be dead. Ensembles of such self-propelled particles, referred to as active matter, show fascinating collective dynamics, like flocking of birds or turbulent-like states in cell colonies. In many systems, for example bacteria swimming in a viscous fluid, the motion of particles is fully overdamped, meaning that any momentum is immediately dissipated by the environment. A particle’s displacement is then effectively given by the forces acting on, and exerted by it. However, Newton’s first law states that, in general, massive objects show persistent motion even in the absence of forces, due to their inertia. Like for flying insects or birds, the time scale of inertial motion can become relevant for the dynamics of particles when the friction experienced within their environment is low. Such systems are considered underdamped. The presented work contributes to the understanding of the collective dynamics of underdamped active matter. Two established coarse-grained continuum models for overdamped systems are extended to explicitly include inertia. Locally averaged fields for particle density, velocity, and direction of self-propulsion describe the dynamics of the resulting models. The original overdamped results are recovered in the low mass limit. In the opposite underdamped regime, it is found that time scales of collective dynamics depend non-trivially on the particle mass. Furthermore, it is shown that introducing inertia into an active system can even lead to additional non-equilibrium states.