Natural soft soils are complex geomaterials: they are structured and exhibit viscous behaviour. The structure of natural soils consists of fabric (i.e. the arrangement of soil particles and particles contacts) and apparent bonding. The fabric of soft clays is often anisotropic and the anisotropy changes during plastic deformations. In addition, the constitutive behaviour of soft soils is time-dependent. Firstly, some recent experimental results on soft natural Finnish clays are shown, demonstrating the complexity of material behaviour that constitutive models for soft clays need to capture. The formulations of recently proposed constitutive models that attempt to represent the soil behaviour under general stress states are then presented. The models are relatively simple hierarchical models, which enable model features to be switched on and off dependent on the problem to be solved. Comparisons with experimental data highlight the importance of accounting for anisotropy and its evolution when modelling the viscous behaviour of soft soils.