  We give a global description of envelopes of geodesic tangents of regular
curves in (not necessarily convex) Riemannian surfaces. We prove that such an
envelope is the union of the curve itself, its inflectional geodesics and its
tangential caustics (formed by the conjugate points to those of the initial
curve along the tangent geodesics). Stable singularities of tangential caustics
and geodesic envelopes are discussed. We also prove the (global) stability of
tangential caustics of close curves in convex closed surfaces under small
deformations of the initial curve and of the ambient metric.
