The pantograph–catenary system is responsible to provide an uninterrupted energy supply to power electric traction railway vehicles. The analysis of the dynamic behaviour of the catenary and pantograph, as well as its interaction, has been the objective of active research to improve energy collection quality. This work proposes an approach for the fully three-dimensional dynamic analysis of pantograph–catenary interaction in general railway tracks including curves. The catenary model and the trajectory of the pantograph base are defined with respect to the track geometry considering the conventional definition used by the rail industry, i.e. the track curvature, cross-level and vertical position. The pantograph is modelled using a multibody formulation being its base motion constrained to follow the generalised trajectory from the railway vehicle roof. The finite element method is used to model the catenary. A co-simulation procedure is set to establish the coupled dynamics of the two systems. In order to demonstrate the methodology, setup models for curved catenaries, analyse modelling implications and highlight applicability, realistic case studies of pantograph–catenary interaction in high-speed rail operations are presented and discussed. In the process, significant differences are found in the dynamic response of the catenary in curved and straight tracks.