In this talk I will discuss some new results on the infinitesimal behavior of 2 dimensional almost minimal surfaces (relevant examples are semi-calibrated currents and section of 3 dimensional minimizing cones). In particular I will show that such surfaces posses a unique tangent cone at every point and I will comment on perspective results concerning their full regularity. This is a joint work with C. De Lellis and L. Spolaor (Zurich).