The perceptual centre (P-centre) is hypothesised to be the unique moment of occurrence of an auditory event. It is furthermore hypothesised that the P-centres induced by an acoustic signal form the temporal pattern which is perceived as rhythm. For this reason researchers of rhythm need a good P-centre model which can be used to prepare rhythmic stimuli or determine the rhythmic properties of produced speech and musical performance. In order to be widely utilised, a good model would be data independent (subject to level and perhaps frequency range calibration), robust, straightforward to implement and in good agreement with all known P-Centre data. For natural speech rhythm research, it is desirable that the model could be directly applied to acoustic signals without requiring explicit segmentation into syllables. This work reviews the existing P-Centre models in detail. With varying degrees of sophistication, these models are shown to use one of just two P-Centre identification strategies: an onset threshold crossing (requiring only short term temporal information) or a weighted sum of features drawn from the entire acoustic signal corresponding to a single auditory event. Each approach is considered in detail and notable differences of prediction between the models are identified for further empirical investigation. A problem which affects the validity of all existing P-Centre models is that they have been trained/fitted and tested with fairly sparse data. (A standard corpus of sounds, labelled with experimentally determined P-Centres, would be enormously useful to all future research in the field.) In the absence of a large P-Centre labelled corpus, a simple test is proposed for coarse subjective evaluation of the perceptual accuracy of any P-centre model. Finally, it is noted that some published P-Centre models are underspecified so that they cannot be implemented without making significant assumptions. This prevents replication and validation of earlier results and reduces confidence in the model. For this reason, it is proposed that any future P-Centre model should be accompanied by reference implementation code.