Task and path planning algorithms for robots in the presence of flows confront a fundamental dichotomy between the continuous and the discrete: task planning algorithms tend to discretize the world and their goals, whereas flows are continuous in nature. This contrast is exemplified in many robotic applications where environmental forces impact navigation and exploiting those flows is critical for the quality of results. In this work, we explore techniques to integrate continuous environmental models with planning methods for robot motion, encompassing high-level task planning and low-level path planning. The main contribution of this thesis is in the formulation of new variants of the Orienteering Problem to address task planning in flows. We begin by first examining a problem that focuses on the high level problem of task planning, but abstracts away the environment and assumes that the low-level path planning is solved independently. While this helps simplify the problem, it neglects to include environmental information which is often fundamentally linked to the vehicle motion. We address this limitation by exploring path planning algorithms in environments that are represented by an external flow field, such as static and time-varying ocean currents. While we cannot control the external currents, our planning method considers the trade-offs between energy efficiency, reward collection, and time budget based on the interplay of the chosen routes, paths, and environment. We expand our analysis to the joint problem of both designing the environmental flows and path planning within the designed flow fields. We explore this problem in the context of controlling magnetically driven milli-robots. We show how we can circumvent the need to solve the inverse dynamics problem by leveraging key features of the generated fields. These features enable us to take a topological approach to solving the joint path planning and motion control problem for magnetically driven robots.