In this survey, we consider two kinds of problems on tube domains over light cones. The first one is related with Poisson-Szeg\"{o} integrals $F$. When $F$ is a bounded real function and satisfies an appropriate smoothness up to the boundary, then $F$ is necessarily the real part of a holomorphic function. The second one is the $L^p$ boundedness of the Bergman projection, for which known positive and negative results leave a gap between them. This gives an illustration of activities within HARP.