Quantum field theory of higher-spin particles is a formidable subject, where Lorentz-invariant approaches tend to lead to a rich gauge-symmetry structure, which serves to preserve the physical number of degrees of freedom. Introducing consistent interactions in such approaches is a non-trivial task, with most higher-spin Lagrangians specified only up to three points. In this talk, I will discuss a new, chiral description for massive higher-spin particles, which in four spacetime dimensions allows to do away with this kind of gauge symmetry. This greatly facilitates the introduction of consistent interactions. I will concentrate on three theories, in which higher-spin matter is coupled to electrodynamics, non-Abelian gauge theory or gravity. These theories are currently the only examples of consistent interacting field theories with massive higher-spin fields. The presented theories are chiral and have simple Lagrangians, resulting in Feynman rules analogous to those of massive scalars. In particular, I will discuss the resulting tree-level scattering amplitudes with two higher-spin matter particles and any number of positive-helicity photons, gluons or gravitons. These amplitudes were previously computed via on-shell recursion and provided evidence for the existence of such simple massive higher-spin theories.