Condition monitoring (CM) describes the continuous observation of a dynamical system or process in order to track the evolution of its state and to detect signs of faults in an early stage. It constitutes the core block for performing fault diagnosis and prognosis, allowing a condition-based assessment of the system and supporting the implementation of an intelligent, cost-effective maintenance policy. This study focuses on the vehicle-based monitoring of railway infrastructure. First, the main concepts related to intelligent maintenance systems and strategies are depicted in a general framework. Later on, the specific application, the railway track–vehicle interaction system, is introduced. Railway vehicle instrumentation for track CM is analyzed, with a special focus on inertial measurement systems. A review of the processing algorithms used for railway monitoring is done, and taxonomy is proposed based on the methodology approach: model-based, data-driven, or hybrid. An analysis of the monitoring algorithms according to the geographical region is also made. It has been found that the railway vocation of each individual region determines the monitoring objectives pursued, as well as the methodological approach and the specific algorithms used. Finally, current trends and research gaps in railway monitoring are identified and outlined.