Spacecraft telemetry data is transferred from satellite to ground control station. The data contains not only information about health status of the satellite but also contains response messages to telecommand (telecommand data is send to spacecraft from ground control station) data. Telemetry data can indicate data error, communication link failure, sensor error, equipment and electronic devices failure. Safety and reliability are provided by telemetry and telecommand data. The most important subjects are safety and reliability for space mission. Therefore, telemetry data should be analyzed and take measures against to attack or unexpected situation. Various intelligent anomaly detection methods are proposed in the literature. Supervised/unsupervised (machine learning) anomaly detection approaches and data mining technology are the most used methods. This paper is a literature review for anomaly detection approaches in space system operation. Anomaly detection techniques have been investigated in the literature, but studies on space domain is quite limited. It is considered to contribute to literature in terms of that.