Abstract. We give an overview of recent results in the area of three-dimensional nonspinning and spinning solitons in some selected models in optics and Bose-Einstein condensate (BEC). We concentrate on the existence and stability of these multiple dimensional localized structures and we reveal the occurence of two cuspidal points in the Hamiltonian (BEC energy) versus soliton norm diagram, resulting in a generic swallowtail bifurcation
