The key aspects of the modeling, algorithm, and architecture for artificial neural nets (ANNs) is reviewed. A programmable systolic array meant for a variety of connectivity patterns for ANNs is proposed. Considered in the design are both the search and learning phases of a class of ANNs. A system-theoretic approach is adopted to elucidate modeling issues for ANNs. On this basis the issues of expressibility and discrimination, fault tolerance and generalization, size of hidden units/layers, interconnectivity patterns, and circuit model for analog ANN implementations are addressed.