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Epithelial tissues possess active matter hallmarks, including self-generated flows and dynamic topological defects associated with multi-cell level order. These sheet-like tissues are also curved and deformable (up to now outside the purview of active matter), and there is evidence that curvature and defects interact to effect morphogenetic changes. This raises the tantalizing idea that some developmental processes rely on coupling between geometry and defects, a cornerstone of equilibrium condensed matter. However, it is not known to what extent out-of-equilibrium driving disrupts the established paradigm. Furthermore, tackling this problem in vivo is not feasible. Our project aims to find physical principles connecting order, activity, and curvature in living matter. We will do this using theory, numerics, and in vitro experiments on monolayers on topographically complex, controlable substrates. With the overriding idea that tissue order couples not only to intrinsic but also extrinsic curvature (usually ignored in theory), we will answer the follow: 1) how does curvature couple to cell rearrangements, cell flows, and the position of defects? 2) What feedback(s) exist between substrate shape and monolayer mechanics? These questions will be addressed in the context of confluent monolayer dynamics and wound-healing-like (free edge) migration, the two types of generic collective cell dynamical behaviors.