In this contribution, I discuss some aspects of the dynamical evolution of supermassive black hole binaries and their accretion discs. Firstly, I discuss the issue of alignment of the spins of the two binary component, which has important implications for the shape of the gravitational wave emitted at merger and for the possibility of a strong recoil of the remnant black hole. Even under the favourable assumption that mass flow through the gap is not inhibited by tidal torque, we demonstrate that differential accretion onto the two components of the systems results in a very different spin evolution of the two black holes. Secondly, I revisit the issue of how much mass can flow within the cavity carved in the disc by an equal mass binary. Recent simulations have shown that the tidal torque of the binary is generally not sufficient to prevent accretion onto the binary component. Here, I demonstrate that such results are heavily dependent on the disc thickness. While for H/R ~ 0.1 (the value adopted in most simulations to date), we reproduce the previous results, we show that as H/R is decreased to ~ 0.01, mass flow through the gap is essentially shut off almost completely. Thirdly, I show numerical simulations of the process of gas squeezing during the merger proper, demonstrating that most of the disc mass is accreted producing a super-Eddington flare.