  This short note has been written as an Oberwolfach report for the workshop
"Differentialgeometrie im Grossen". We discuss properties of metric spaces that
at almost all points admit a tangent metric space. We explain why, under some
mild assumptions, the tangents are almost surely subFinsler Carnot groups. We
mention several situations when the tangents are Euclidean spaces, but the
initial metric spaces are quite pathological.
