I will present an overview of the family of quadratic rational maps with a 2- periodic superattracting orbit. Many of these maps can be described as the mating of the basilica with a quadratic polynomial. For this reason, the family has attracted much recent attention, and the parameter space picture is now nearly completely understood. I will survey the known results, with particular emphasis on my own contribution to the topic: the mateability of Siegel quadratic polynomials of bounded type with the basilica polynomial.