Continuous spin particles are massless irreducible representations of the Poincare’ group, with a non-vanishing Pauli-Lubanski casimir operator. They differ from ordinary massless particles as carrying infinitely many helicities, for any given 4-momentum. We discuss how to construct on-shell 3- and 4-point scattering amplitudes involving continuous spin particles that are well-behaved in the high energy limit. We discuss their main features and constrast their properties with ordinary massless particles.