The development of a navigation system is one of the major challenges in building a fully autonomous platform. Full autonomy requires a dependable navigation capability not only in a perfect situation with clear GPS signals but also in situations, where the GPS is unreliable. Therefore, self-contained odometry systems have attracted much attention recently. This paper provides a general and comprehensive overview of the state of the art in the field of self-contained, i.e., GPS denied odometry systems, and identifies the out-coming challenges that demand further research in future. Self-contained odometry methods are categorized into five main types, i.e., wheel, inertial, laser, radar, and visual, where such categorization is based on the type of the sensor data being used for the odometry. Most of the research in the field is focused on analyzing the sensor data exhaustively or partially to extract the vehicle pose. Different combinations and fusions of sensor data in a tightly/loosely coupled manner and with filtering or optimizing fusion method have been investigated. We analyze the advantages and weaknesses of each approach in terms of different evaluation metrics, such as performance, response time, energy efficiency, and accuracy, which can be a useful guideline for researchers and engineers in the field. In the end, some future research challenges in the field are discussed.