The worldwide increase in frequency of traffic for passenger trains and the rise of freight trains over the recent years necessitate the more intense deployment of track monitoring and rail inspection procedures. The wheel-rail contact forces, induced by the static axle loads of the vehicle and the dynamic effects of ground-borne vibration coming from the track superstructure, have been a significant factor contributing to the degradation of the railway track system. Measurements of track irregularities have been applied since the early days of railway engineering to reveal the current condition and quality of railway lines. Track geometry is a term used to collectively refer to the measurable parameters including the faults of railway tracks and rails. This paper is aiming to review the characteristics of compact inertial measurement systems (IMUs), their components, installation, the basic measures of the quality of the track using motion sensors, like accelerometers, gyroscopes and other sensing devices mounted on different places of the vehicle.Additionally, the paper briefly discusses the fundamentals of inertial navigation, the kinematics of the translational and rotational train motions to obtain orientation, velocity and position information.