Hilbert's fourth problem asks for the construction and the study of metrics on subsets of projective space for which the projective line segments are geodesics. Abstract: Several solutions of the problem  were given so far, depending on more precise interpretations of this problem, with various additional conditions satisfied   We review some of these  major developments as well as other important results related to Hilbert's problem, mentioning recent results and connections with several branches of mathematics, including Riemannian geometry, the foundations of mathematics, the calculus of variations, metric geometry and Finsler geometry.