Yield stress fluids (YSF) exhibit strongly non-linear rheological characteristics. As a consequence, they develop original flow features (as compared to simple fluids) under various boundary conditions. This paper reviews and analyzes the characteristics of a series of slow flows (just beyond yielding) under more or less complex conditions (simple shear flow, flow through a cavity, dip-coating, blade-coating, Rayleigh-Taylor instability, Saffman-Taylor instability) and highlights some of their common original characteristics: (i) a transition from a solid regime to a flowing regime which does not correspond to a true "liquid state," the flow in this regime may rather be seen as a succession of solid states during very large deformation; (ii) a strong tendency to localization of the yielded regions in some small region of the material while the rest of the material undergoes some deformation in its solid state; (iii) the deformation of YSF interface with another fluid, in the form of fingers tending to penetrate the material via a local liquefaction process. Finally, these observations suggest that slow flows of YSF are a kind of extension of plastic flows for very large deformations and without irreversible changes of the structure. This suggests that the field of plasticity and the field of slow flows of YSF could benefit from each other.