We study the stability and electronic properties of intrinsic point defects, vacancy and self-interstitial, in mono and bilayer phosphorene. We calculate the formation energies, quasiparticle defect states, and charge transition levels (CTLs) of these defects using ab initio density functional theory (DFT) and GW approximation to the electron self-energy. Using the DFT+GW two paths formalism for studying interstitial in monolayer phosphorene, we show that with the inclusion of electrostatic corrections CTLs can be calculated reliably. Our calculations show that all the native point defects have low formation energies 0.9-1.6 eV in neutral state. Furthermore, we find that vacancy in phosphorene behaves as an acceptorlike defect which can explain the $p$-type conductivity in phosphorene. On the other hand, interstitial can show both acceptor- and donorlike behavior.