Bogies are key subsystems for rolling stock safety and, therefore, meaningful and objective data concerning their condition is of paramount importance for railway operation. These subsystems experience severe service conditions causing wear, damage and degradation of components and affecting the vibrations to which the passengers are exposed. As such, safe and reliable operation, together with a high level of comfort for the passengers, can only be assured by an in-depth, data-based and comprehensive maintenance of the bogie components. In this perspective, advanced health monitoring of the running gear plays a fundamental role as the enabler for condition-based maintenance strategies. This paper reports about work performed in the RUN2Rail project aimed at formulating new concepts for the condition monitoring of the running gear. Three case studies are addressed: wheelsets, powertrain and suspension components. For these cases, the suitable choice and location of sensors is investigated and innovative fault detection and fault classification methods are proposed and preliminarily validated by means of numerical experiments and laboratory tests. A concise outline of the impacts and benefits of each proposed condition monitoring application is also provided.