Contact structure among livestock populations influences the transmission of infectious agents among them. Models simulating realistic contact networks therefore have important applications for generating insights relevant to livestock diseases. This systematic review identifies and compares such models, their applications, data sources and how their validity was assessed. From 52 publications, 37 models were identified comprising seven model frameworks. These included mathematical models (n = 8; including generalized random graphs, scale-free, Watts-Strogatz and spatial models), agent-based models (n = 8), radiation models (n = 1) (collectively, considered 'mechanistic'), gravity models (n = 4), exponential random graph models (n = 9), other forms of statistical model (n = 6) (statistical) and random forests (n = 1) (machine learning). Overall, nearly half of the models were used as inputs for network-based epidemiological models. In all models, edges represented livestock movements, sometimes alongside other forms of contact. Statistical models were often applied to infer factors associated with network formation (n = 12). Mechanistic models were commonly applied to assess the interaction between network structure and disease dissemination (n = 6). Mechanistic, statistical and machine learning models were all applied to generate networks given limited data (n = 13). There was considerable variation in the approaches used for model validation. Finally, we discuss the relative strengths and weaknesses of model frameworks in different use cases.