Networks are used to represent relationships between entities in many complex systems, spanning from online social networks to biological cell development and brain activity. These networks model relationships which present various challenges. In many cases, relationships between entities are unambiguously known: are two users friends in a social network? Do two researchers collaborate on a published paper? Do two road segments in a transportation system intersect? These are unambiguous and directly observable in the system in question. In most cases, relationship between nodes are not directly observable and must be inferred: does one gene regulate the expression of another? Do two animals who physically co-locate have a social bond? Who infected whom in a disease outbreak? Existing approaches use specialized knowledge in different home domains to infer and measure the goodness of inferred network for a specific task. However, current research lacks a rigorous validation framework which employs standard statistical validation. In this survey, we examine how network representations are learned from non-network data, the variety of questions and tasks on these data over several domains, and validation strategies for measuring the inferred network’s capability of answering questions on the original system of interest. Network Structure Inference, A Survey: Motivations, Methods, and Applications