I will discuss a recent result in real algebraic geometry: a wall crossing formula for central projections defined on submanifolds of a real projective space. This formula gives the jump of the degree of such a projection when the center of the projection varies. The fact that the degree depends on the projection is a new phenomenon, specific to real algebraic geometry. We illustrate this phenomenon in many interesting situations. The crucial assumption on the class of maps we consider is relative orientability, a condition which allows us to define a $\Z$-valued degree map in a coherent way. I will discuss an interesting consequence of this result: a very general "no gap" theorem for the values of the degree map.