Context -Software process simulation modelling (SPSM) captures the dynamic behavior and uncertainty in the software process. Existing literature has conflicting claims about the practical usefulness of SPSM: SPSM is useful and has an industrial impact; SPSM is useful and has no industrial impact yet; SPSM is not useful and has little potential for industry. Objective -To assess the conflicting standpoints on the usefulness of SPSM. Method -A systematic literature review was performed to identify, assess and aggregate empirical evidence on the usefulness of SPSM. Results -In the primary studies, to date, the persistent trend is that of proof-of-concept applications of software process simulation for various purposes (e.g. estimation, training, process improvement, etc.). They score poorly on the stated quality criteria. Also only a few studies report some initial evaluation of the simulation models for the intended purposes. Conclusion -There is a lack of conclusive evidence to substantiate the claimed usefulness of SPSM for any of the intended purposes. A few studies that report the cost of applying simulation do not support the claim that it is an inexpensive method. Furthermore, there is a paramount need for improvement in conducting and reporting simulation studies with an emphasis on evaluation against the intended purpose.