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Geohistorical records, either stratigraphic sections, boreholes, ice cores, or archaeological sites, are inherently complex. Despite their limitations, the high-dimensional and spatiotemporally resolved data retrieved from individual geohistorical records allow for evaluation of past biotic responses to natural and human-induced environmental changes. Network analysis is becoming an increasingly popular alternative for modelling the dynamics of geohistorical data. However, the complexity of geohistorical data raises questions about the limitations of standard network models widely used in paleobiology research. They risk obscuring large-scale patterns by washing out higher-order node interactions when assuming independent pairwise links. Recently introduced higher-order representations and models better suited for the complex relational structure of geohistorical data provide an opportunity to move paleobiology research beyond these challenges. Higher-order networks can represent the spatiotemporal constraints on the information paths underlying geohistorical data, capturing the high-dimensional patterns more accurately. Here we describe how to design higher-order network models of geohistorical data, address some practical decisions involved in modeling complex dependencies, and discuss critical methodological and conceptual issues that make it difficult to compare results across studies in the growing body of network paleobiology. We illustrate multilayer networks, hypergraphs, and varying Markov time models through case studies on the fossil record from continental shelf ecosystems and delineate future research directions for current challenges in the emerging field of network paleobiology.