The first part of the talk is related to the classification of bifurcations in generic $k$-parameter families of vector fields in the plane. This theory is at the very beginning of its construction. Majority of statements consists of problems and conjectures.

The second part will be related to the study of the bifurcation diagrams in such families. These diagrams are defined as the sets in the parameter space of the family for which the corresponding vector fields are not structurally stable. Quite unexpected germs of bifurcation diagrams occur even in the two and three parameter families. In four parameter families they are expected to have numeric invariants.

All the necessary definitions will be given.