Increased demand for railway transportation is creating a need for higher train speeds and axle loads. These, in turn, increase the likelihood of track degradation and failures. Modelling the degradation behaviour of track geometry and development of applicable and effective maintenance strategies has become a challenging concern for railway infrastructure managers. During the last three decades, a number of track geometry degradation and maintenance modelling approaches have been developed to predict and improve the railway track geometry condition. In this paper, existing track geometry measures are identified and discussed. Available models for track geometry degradation are reviewed and classified. Tamping recovery models are also reviewed and discussed to identify the issues and challenges of different available methodologies and models. Existing track geometry maintenance models are reviewed and critical observations on each contribution are provided. The most important track maintenance scheduling models are identified and discussed. Finally, the paper provides directions for further research.