M-harmonic functions on the complex unit ball are those that are annihilated by the Moebius-invariant Laplacian. While holomorphic and harmonic Bergman kernels with respect to standard weights on the ball have by now been well-known objects already for decades, their M-harmonic counterparts turn out to be much more elusive. We survey recent advances for the unit ball and briefly indicate what further problems occur for more general situations.