Modular robot manipulators are composed of a collection of independent modules, each capable of both sensing and actuation. These modules can be connected in different morphologies to complete user-specified tasks, and can be easily reconfigured to achieve otherwise infeasible tasks. Thus, modular robot manipulators are more robust (a module can be simply replaced in case of failure) and versatile (able to perform a wide range of tasks) than conventional off-the-shelf robot arms. However, these potential advantages can only be realized if we can efficiently choose an appropriate design (structure) and behavior (controls) from a large search space of possible configurations and control sequences for a given task. In this dissertation, I will present my work on frameworks for automated synthesis of correct-by-construction structure and controls for modular manipulators from high-level specifications for a variety of tasks including trajectory following in the presence of obstacles and carrying payloads between a set of points in the workspace. I will also present new strategies which can be employed to respond to situations in which no design can be found (e.g. infeasible tasks). Finally, I will validate the capabilities of this system through both simulations and hardware experiments demonstrating modular manipulators performing complex tasks, such as drawing and wiping off a table, in a constrained real-world environment.