I will discuss a systematic way of taking into account non-perturbative effects on the closed string scattering amplitudes in c=1 string theory, and present a recent proposal on the corresponding non-perturbative completion of the dual matrix quantum mechanics.

I will discuss FZZT branes and long strings in c=1 string theory, and the dual description of the latter in non-singlet sectors of the matrix quantum mechanics. I will present highly nontrivial evidences for the duality at the level of perturbative scattering amplitudes, and discuss implications on black holes in c=1 string theory and their matrix model duals.