The emerging technology of acoustic charge transport (ACT), which has enabled the implementation of powerful signal processors capable of handling high-speed RF and microwave signals in their natural analog domain, is reviewed. The development of ACT technology has led to the implementation of fully programmable analog signal processors capable of performing over 45 billion multiply-and-accumulate operations per second. These processors are finding application as adaptive filters and equalizers in a variety of commercial and military systems. The operation and performance capabilities of the ACT device are described, and seven applications now under development are discussed.