We present a theoretical investigation of the effects of low-frequency vibrations on the motion of two-dimensional droplets on heterogeneous substrates in the presence of gravity and substrate heterogeneities, both chemical and topographical. A combined analytical and numerical approach is undertaken, extending the work of Savva & Kalliadasis on inclined heterogeneous substrates (J. Fluid Mech., vol. 725, 2013, p. 462) to include the effects of substrate vibrations and obtain, via a matching procedure and under the quasistatic assumption, evolution equations for the moving fronts. These equations are then invoked in a wide variety of case studies. It is demonstrated that vertically vibrated horizontal ratcheted substrates can induce unidirectional motion; for inclined substrates, we focus on a number of qualitative aspects of the peculiar vibration-induced climbing of droplets reported in experiments by Brunet, Eggers & Deegan (Phys. Rev. Lett., vol. 99, 2007, 144501). We examine the effects of weak inertia on the dynamics, deduce analytical criteria for the uphill motion in the limit of weak gravitational and vibrational effects, and demonstrate that substrate heterogeneities may be utilised to enhance droplet transport.