Digital microfluidics has become a popular tool for biochemical and biomedical applications. However, its current format is restricted to actuation of droplets on a single plane. Here, we introduce a new method for fluid handling on flexible devices, which we have termed all-terrain droplet actuation (ATDA). We show that ATDA can be used to manipulate droplets across a wide range of geometries, including inclined, declined, vertical, twisted, and upside-down architectures. These new geometries enable flexible, straightforward integration of distinct physicochemical environments on monolithic devices. To illustrate this capacity, we developed temperature- and oxygen-sensitive colorimetric sensors, as well as an automated method for selective enrichment of DNA from a heterogeneous mixture. We anticipate that ATDA will be a useful new tool in the growing trend toward laboratory miniaturization.