Network-based representation has quickly emerged as the norm in representing rich interactions in complex systems. For example, given the trajectories of ships, a global shipping network can be constructed by assigning port-to-port traffic as edge weights. However, the conventional first-order (Markov property) networks thus built captures only pairwise shipping traffic between ports, disregarding the fact that ship movements can depend on multiple previous steps. The loss of information when representing raw data as networks can lead to inaccurate results in the downstream network analyses. In this talk I will introduce the Higher-order Network (HON), which remedies the gap between big data and the network representation by embedding higher-order dependencies in the network. I will show how existing network algorithms including clustering, ranking, and anomaly detection can be directly used on HON without modification, and influence observations in interdisciplinary applications such as modeling global shipping and web user browsing behavior.