In this talk we will consider the Schroedinger operator on a finite interval with an $L^1$-potential. Borg's two spectra theorem says that the potential can be uniquely recovered from two spectra. By another classical result of Marchenko, the potential can be uniquely recovered from the spectral measure or Weyl $m$-function. After a brief review of inverse spectral theory of one dimensional Schroedinger operators, we will discuss the following mixed spectral problem as a complex analysis problem: Can one spectrum together with subsets of another spectrum and morning constants uniquely determine the potential?