In the past few decades, Coxian phase-type distributions have become increasingly more popular as a means of representing survival times in healthcare models. In particular, they are considered suitable for modelling the length of stay of patients in hospital and more recently for modelling the patient waiting times in Accident and Emergency Departments. However, problems have arisen in how to accurately estimate the parameters of the model from healthcare data. This paper examines the various approaches and considers the recent developments in fitting the Coxian phase-type distribution.