Galaxies and the dark matter halos in which they reside are intrinsically connected. That relationship holds information about key processes in galaxy and structure formation. In this talk, I will consider how the galaxy-halo connection depends on position within the cosmic web - the familiar decomposition of large-scale structure in filaments, knots and voids. Simulations demonstrate the various ways in which the cosmic web modulates the growth and dynamics of halos. The extent to which the cosmic web impacts on galaxies is more difficult to establish. For example, galaxies might be sensitive only to the evolution of the host halo, in which case any effect of the cosmic web on galaxies is secondary, and can be inferred from the halo's history. There is evidence, however - from simulations and observations - that the cosmic web also impacts on the evolution of galaxies via the effect it has on the broader gas ecosystem in which they are embedded, as well as through "pre-processing" effects on group scale. So, how should we think of the cosmic web in its role as a transformative agent of galaxies? And what physical processes can we convincingly constrain from observations and simulations? In this talk I highlight recent work that addresses these questions.