There are examples of branching processes in varying environment (BPVE) , which do not fit to our ideas on branching processes and show exotic behaviour like two different rates of exponential growth. In particular a classification in the spirit of standard Galton-Watson processes seemed to be beyond reach. In the talk we explain that on the contrary a mild uniformity condition is sufficient to exclude exotic behaviour, to obtain theorems analog to those known for Galton-Watson processes, and to arrive at a classification of BPVEs.