Graph or network abstractions are an important foundation for the computational modeling of complex systems. They help us to model (and control) power grids, transportation and communication infrastructures, to study dynamical processes in computational physics and systems biology, to analyse social and economic networks, and to extract knowledge from large corpora of relational data. While this potential of the network perspective is undisputed, advances in data sensing and collection increasingly provide us with high-dimensional, temporal, and noisy data on real systems. The complex characteristics of such data sources pose fundamental challenges for data-driven modelling. They question the validity of network models of complex systems and pose a threat for interdisciplinary applications of data science and machine learning. To address these challenges, I introduce graphical modelling techniques that account for the complex characteristics of real-world data on complex systems. I demonstrate this in time series data on systems with dynamic topologies. Current approaches to model the topology of such systems discard information on the timing and ordering of interactions, which however determines who can influence whom. To solve this issue, I introduce a novel statistical modelling framework that (i) generalises standard network abstractions towards multi-order graphical models, and (ii) uses principled model selection techniques to achieve an optimal balance between explanatory power and model complexity. This framework advances the theoretical foundation of data science and network analysis and sheds light on the important question when network abstractions of complex data are actually justified. It opens broad perspective for the modelling of dynamical processes in natural and engineered systems and is the basis for a new generation of data mining and machine learning techniques that account both for temporal and topological characteristics in real-world data.