In this paper, we report on our recent findings concerning the structure of complex coacervate core micelles composed of two types of (complementary) block copolymers. Both copolymers have a polyelectrolyte (one cationic and the other anionic) block combined with a neutral one. The opposite charges attract and form a close-to-electroneutral core. The two neutral blocks form the corona of the micelles. Here, we focus on the structure of the corona, which among other possibilities assumes the Janus configuration. Corresponding self-consistent field calculations confirm the rich behaviour of these systems. Unless the solvent quality of one of the corona chains is poor, we do not expect an onion-like corona with a clear interface between the layers. Disparities in chain length and solvent quality may only lead to gradual differences (local enrichments) in radial distributions. In the case that both corona chains are in good solvent, an unfavourable mixing of the two chains leads to the formation of Janus micelles, where the two blocks occupy different hemispheres. The interface that separates the two regions exerts a force on the core, which will deform when the core surface tension is not too high. In line with experimental results, the core flattens like a disk and the corona chains extend most in the direction of the poles.