Spatial solitons are the most fundamental entities of the interaction between light and nonlinear conservative media. Due to the waveguide induced into the medium, spatial solitons could potentially play a prominent role in optical data transmission. Soliton stability is a complex problem, that depends upon numerous factors. Identifying the unstable eigenmodes allows for a deeper insight into the mechanisms that stabilise/destabilise spatial solitons. Due to the lack of analytical tools, the eigenmodes are most commonly identified by means of numerical calculations. The fundamental differences between symmetry-conserving and symmetry-breaking instabilities are being highlighted. Changing the degree of coherence of the light used is shown to have severe effects on the stability of the solitons. Furthermore, the stability of counterpropagating solitons is investigated. Due to the changed boundary conditions, counterpropagating solitons show entirely different instabilities as compared to their copropagating counterparts. We observe temporal dynamics of the system that can be periodic or irregular. A strongly simplified analytical model allows for an estimate of the stability threshold of counterpropagating solitons.