The original cubic interaction terms for higher spin gauge fields in four dimensions and their reformulation using Fock space vertex operators is reviewed. As a new result, the complete list of all cubic vertex functions in D=4 is derived. It is observed, contrary to what would have been expected, that the non-linear dynamical Poincar\'e transformations do not restrict the cubic interactions beyond what is required by kinematics. The role of the SU(1,1) algebra of tracelessness constraints is clarified. It is shown that higher spin fields couple non-minimally to gravity at the cubic level in D=4 light-front dynamics. Based on a detailed analysis of the structure of the light-front Poincar\'e algebra, the formalism is then generalized to all orders in the interaction. The interacting theory, being a deformation of the free theory, takes the form of a strongly homotopy Lie algebra. It is conjectured that the ensuing recursive equations, if they can be explicitly solved, will encode all interaction data into a denumerable set of functions of p+, the overall transverse momentum structure being fixed already at the kinematical level.