Animals exploit time to survive in the world. Temporal information is required for higher-level cognitive abilities such as planning, decision making, communication, and effective cooperation. Since time is an inseparable part of cognition, there is a growing interest in the artificial intelligence approach to subjective time, which has a possibility of advancing the field. The current survey study aims to provide researchers with an interdisciplinary perspective on time perception. Firstly, we introduce a brief background from the psychology and neuroscience literature, covering the characteristics and models of time perception and related abilities. Secondly, we summarize the emergent computational and robotic models of time perception. A general overview to the literature reveals that a substantial amount of timing models are based on a dedicated time processing like the emergence of a clock-like mechanism from the neural network dynamics and reveal a relationship between the embodiment and time perception. We also notice that most models of timing are developed for either sensory timing (i.e. ability to assess an interval) or motor timing (i.e. ability to reproduce an interval). The number of timing models capable of retrospective timing, which is the ability to track time without paying attention, is insufficient. In this light, we discuss the possible research directions to promote interdisciplinary collaboration in the field of time perception.