Semiconductor nanowires (NWs) represent a unique system for exploring phenomena at the nanoscale and are also expected to play a critical role in future electronic and optoelectronic devices. Here we review recent advances in growth, characterization, assembly and integration of chemically synthesized, atomic scale semiconductor NWs. We first introduce a general scheme based on a metal-cluster catalyzed vapour-liquid-solid growth mechanism for the synthesis of a broad range of NWs and nanowire heterostructures with precisely controlled chemical composition and physical dimension. Such controlled growth in turn results in controlled electrical and optical properties. Subsequently, we discuss novel properties associated with these one-dimensional (1D) structures such as discrete 1D subbands formation and Coulomb blockade effects as well as ballistic transport and many-body phenomena. Room-temperature high-performance electrical and optical devices will then be discussed at the single- or few-nanowire level. We will then explore methods to assemble and integrate NWs into large-scale functional circuits and real-world applications, examples including high-performance DC/RF circuits and flexible electronics. Prospects of a fundamentally different 'bottom-up' paradigm, in which functionalities are coded during growth and circuits are formed via self-assembly, will also be briefly discussed.