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 object of active research to improve the 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. Both 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., curvature, cross level and vertical position of the track. The pantograph is modelled using a 3D multibody formulation being its base motion constrained to follow the generalized trajectory from the top of a railway vehicle. The finite element method is used to model the catenary. A co-simulation procedure is set to allow for the coupled dynamics of the two systems. In order to demonstrate the methodology, setting up models for curved catenaries, analyse their modelling implications and highlight applicability, realistic case studies of pantograph-catenary interaction in high-speed rail operations are presented and discussed. In the process there are found significant differences on the dynamic response of the catenary in curved and straight tracks.