Programmable force vector fields can be used to control a variety of flexible planar parts feeders such as massively-parallel micro actuator arrays or transversely vibrating (macroscopic) plates. These new automation designs promise great flexibility, speed, and dexterity---they may be employed to position, orient, singulate, sort, feed, and assemble parts. A wealth of geometric and algorithmic problems arise in the control and programming of manipulation systems with many independent actuators. The theory of programmable force fields represents the first systematic attack on massively-parallel distributed manipulation based on geometric and physical reasoning. We show how to develop combinatorially precise planning algorithms that synthesize force field strategies for controlling a very large number of distributed actuators in a principled, geometric, task-level fashion. When a part is placed on our devices, the programmed force field induces a force and moment upon it. Over time, the part may come to rest in a dynamic equilibrium state. By chaining together sequences of force fields, the equilibrium states of a part in the field may be cascaded to obtain a desired final state. The resulting strategies require no sensing and enjoy efficient planning algorithms. This thesis introduces new experimental devices that can implement programmable force fields. In particular, we describe the M-Chip (Manipulation Chip), a massively-parallel array of programmable micro-motion pixels. Both the M-Chip, as well as macroscopic devices such as transversely vibrating plates, may be programmed with force fields, and their behavior predicted and controlled using our equilibrium analysis. We demonstrate lower bounds (i.e., impossibility results) on what the devices cannot do, and results on a classification of control strategies yielding design criteria by which well-behaved manipulation strategies may be developed. We define composition operators to build complex strategies from simple ones, and show the resulting fields are also well-behaved. Finally, we consider parts feeders that can only implement a very limited ``vocabulary'' of force fields. We show how to plan and execute parts-posing and orienting strategies for these devices, but with a significant increase in planning complexity and some sacrifice in completeness guarantees. We discuss the tradeoff between mechanical complexity and planning complexity.