This thesis presents and justifies a framework for programming real-time signal processing systems. The framework extends the existing "block-diagram" programming model; it has three components: a very high-level textual language, a visual language, and the dataflow process network model of computation. The dataflow process network model, although widely-used, lacks a formal description, and I provide a semantics for it. The formal work leads into a new form of actor. Having established the semantics of dataflow processes, the functional language Haskell is layered above this model, providing powerful features — notably polymorphism, higher-order functions, and algebraic program transformation — absent in block-diagram systems. A visual equivalent notation for Haskell, Visual Haskell, ensures that this power does not exclude the "intuitive" appeal of visual interfaces; with some intelligent layout and suggestive icons, a Visual Haskell program can be made to look very like a block dia...