We are studying the transport properties of hybrid S-TI-S devices fabricated by depositing superconductor electrodes onto topological insulators. In top-gated Nb-Bi2Se3-Nb junctions, we have measured the Josephson supercurrent and conductance as a function of geometry, temperature, and gate voltage in order to determine the nature of the charge transport. The supercurrent exhibits a sharp drop as a function of gate doping that may be explained by the relocation of the topological surface state from above to below the trivial conducting surface states formed by band-banding near the surface. We find that the magnetic field modulation of the supercurrent in Josephson junctions and dc SQUIDs exhibits anomalous features that are consistent with a sin(ϕ/2) component in the current-phase relation that we attribute to the presence of low energy Andreev-bound states and possibly Majorana modes in the junction. We present a model for the current-phase relation that describes many of the observed features and predicts the nucleation and motion of these states with applied field. We have also measured transport in TI-S-TI structures that allows us to search for crossed Andreev reflection and electron co-tunneling processes allowed by Cooper pair coherence. We find an anomalous asymmetry in the nonlocal transport that we attribute to a chiral p-wave superconducting order parameter component induced in the topological insulator by the superconducting contact.