Matter consists of charges that interact with electromagnetic fields. This interaction gives rise to mechanical forces that can be utilized to control matter. Based on Maxwell’s equations we derive a continuity equation for linear momentum, which allows us to calculate the force exerted by an optical field on an arbitrary object. We derive the radiation pressure acting on an irradiated surface and show that if the surface is in motion, it will experience a viscous force known as radiation damping. We then investigate the force acting on a tiny particle characterized by its polarizability $\alpha$, and split this force into conservative and nonconservative parts. This leads to the concepts of gradient and scattering forces, which are widely used for the manipulation of atoms, molecules, and nanoparticles. We discuss the properties of optical tweezers and derive the torque exerted on a particle by a circularly polarized light beam. Finally, we discuss how the motion of a vacuum-trapped particle can be amplified or cooled via feedback and touch on the limits imposed by zero-point fluctuations.