We revisit T-duality transformations for the open string via Buscher's procedure and work-out technical details which have been missing so far in the literature. We take into account non-trivial topologies of the world-sheet, we consider T-duality along directions with Neumann as well as Dirichlet boundary conditions, and we include collective T-duality along multiple directions. We illustrate this formalism with the example of the three-torus with H-flux and its T-dual backgrounds, and we discuss global properties of open-string boundary conditions on such spaces.