Optimisation design of composite structures requires an accurate predictive model for forming behaviour. The simulation process contains a number of model parameters which include transverse and longitudinal viscosities of continuous fibre-reinforced viscous composites, fundamental to predicting the shear rheology. Shearing the unidirectional composite along the fibre direction gives a measure of the longitudinal viscosity (LV), whilst shearing across or transverse to the fibre direction gives a measure of the transverse viscosity (TV). Numerous experimental work was conducted in the past to measure these two viscosities for various materials. However, conflicting measurements by different test methods were obtained and these apparent discrepancies had not yet been systematically investigated in any single study. This paper reviews previous work on characterisation techniques to further understand the cause of such discrepancy, and hence to improve measurement accuracy, which would benefit future work on theoretical modelling of the composite viscosities and optimisation simulation of composites forming. Some important findings, such as effects of resin-rich areas, contributory factors of elastic effects, non-Newtonian behaviour for composites with Newtonian matrix, aspect ratio and end effects of test samples, geometry effects of fibres and fibre rearrangement during shearing, existence of a mathematical relationship between LV and TV and necessary benchmarking exercise using Newtonian matrix composites, were summarised.