The increasing use of linear hybrid cellular automata (LHCA) in VLSI design and test and other applications for such purposes as pseudo random pattern generation has made it important for users to understand their design, use and properties. In this tutorial paper, the background for cellular automata is explained, and a recent synthesis algorithm with low complexity, which solves the problem of nding a particular linear hybrid cellular automata, is described. LHCA have powerful concatenation and partitioning properties allowing several smaller maximal length LHCA to be combined into a much larger maximal length LHCA. Their performance in this regard is compared with linear feedback shift registers (LFSRs), which do not have quite as much exibility. The basis for LHCA being better generators than LFSRs for testing delay type faults is explained by showing the richer nature of the transition pairs generated by the LHCA.