The determinantal point processes arise naturally from different areas such as random matrices, representation theory, random graphs and zeros of holomorphic functions etc. In this talk, we will briefly talk about determinantal point processes related to spaces of holomorphic functions, in particular, we will discuss some results concerning the conditional measures, rigidity property and the Olshanskis problem on this area. The talk will be based on several works joint with Alexander Bufetov, Alexander Shamov and Shilei Fan.