We present some recent results on the double bubble problem for the anisotropic perimeter Pα, α ≥ 0 associated with the Grushin plane. The problem consists in finding the best configurations of two regions in the plane enclosing given volumes, in order to minimize their total anisotropic perimeter. When $\alpha=0$, the Grushin plane is just the Euclidean one. If $\alpha\neq 0$, this is a Riemannian structure that degenerate to a sub-Riemannian one on an axis. We prove existence of minimizers and characterize them, in the case of two equal given volumes, and under the assumption that the interface between the bubbles lays on one axis. In particular, we characterize the angles between the bubbles, providing a nice relation with the regularity theory for (Riemannian) perimeter minimizers. In conclusion, in the case $\alpha=1$, minimal double bubbles with interface on the vertical axis have perimeter strictly greater then the ones having interface on the horizontal one: we interpret this fact in terms of isoperimetric sets. Joint work with G. Stefani (SNS, Pisa).