Systolic arrays are descendants of array-like architectures such as iterative arrays, cellular automata and processor arrays. A systolic array is a network of processors that rhythmically compute and pass data through the system. The seminal paper by Kung and Leiserson defines systolic arrays as devices with simple and regular geometries and data paths with pipelining as general methods of using these structures.

The systolic array paradigm is the counterpart of the von Neuman paradigm. While the von Neuman architecture is instruction-stream-driven by an instruction counter, the systolic array architecture is data-stream-driven by data counters. A systolic array is composed of matrix-like rows of units called cells or Data Processing Units (DPUs). DPUs operation is transport-triggered, i.e., triggered by the arrival of a data object. The DPUs are connected in a mesh-like topology (often two-dimensional). Each DPU is connected to a small number of nearest neighbor DPUs and performs a sequence of operations on data that flows between them. Often different data streams flow across the mesh in different directions. Early on, Kung identified the main strength of systolic arrays as addressing the problem of I/O bottleneck:

Thus, a problem what was originally compute-bound can become I/O-bound during its execution. This unfortunate situation is the result of a mismatch between the computation and the architecture. Systolic architectures, which ensure multiple computations per memory access, can speed up compute-bound computations without increasing I/O requirements.