The fundamental mechanisms of complex neural computation remain largely unknown, especially in respect to the characteristics of distinct neural circuits within the mammalian brain. The bottom-up approach of building well-defined neural networks with controlled topology has immense promise for improved reproducibility and increased target selectivity and response of drug action, along with hopes to unravel the relationships between functional connectivity and its imprinted physiological and pathological functions. In this review, we summarize the different approaches available for engineering neural networks treated analogously to a mathematical graph consisting of cell bodies and axons as nodes and edges, respectively. After discussing the advances and limitations of the current techniques in terms of cell placement to the nodes and guiding the growth of axons to connect them, the basic properties of patterned networks are analyzed in respect to cell survival and activity dynamics, and compared to that of in vivo and random in vitro cultures. Besides the fundamental scientific interest and relevance to drug and toxicology tests, we also visualize the possible applications of such engineered networks. The review concludes by comparing the possibilities and limitations of the different methods for realizing in vitro engineered neural networks in 2D.