A fundamental result in differential geometry is the resolution of the Weyl problem: every metric of positive curvature on the 2-sphere admits a unique realization at the boundary of a strictly convex body in the Euclidean 3-space. This problem has a polyhedral counterpart, called the Alexandrov theorem: every convex Euclidean cone-metric on the 2-sphere admits a unique realization at the boundary of a convex polyhedron in the Euclidean 3-space. The work of Thurston from 70s highlighted the ubiquity and the diversity of hyperbolic manifolds among 3-dimensional ones. Hyperbolic 3-manifolds with convex boundary constitute a large and interesting class to study from various perspectives. In 90’s-00’s an analogue of the Weyl problem for hyperbolic 3-manifolds with smooth strictly convex boundary was resolved in the works of Labourie and Schlenker. Curiously enough, a polyhedral counterpart was not known until recently. One of the reasons is that some metrics on the boundary of such 3-manifolds that are «intrinsically polyhedral» admit not so polyhedral realizations, which are somewhat more difficult to handle. In my talk I will review these problems and will present a recent proof of the respective polyhedral result (the rigidity is shown in a generic case).