Key features of higher-spin extensions of ordinary gravity are briefly reviewed. The introduction of consistent interactions between massless fields with spin higher than two is a notoriously difficult challenge of modern theoretical physics, which is well-motivated by string theory and holographic duality. Particular emphasis is put on the fact that the kinematical foundations of the subject are firmly grounded on rigorous mathematical results. Moreover, the introduction of higher-spin interactions admits several formulations that make the former a well-posed problem in mathematical physics. A quick tour is offered through the main results and open issues in this area of research.