We present generic constructions of stateful public key encryption (StPE). We build several new StPE schemes and explain existing ones using our generic constructions. Of the new StPE schemes, two schemes are built using the “identity-based technique” whereby one can construct public key encryption (PKE) schemes secure against chosen ciphertext attack in the standard model from identity-based encryption (IBE) schemes. These StPE schemes provide a positive answer to Bellare et al.’s open question on whether stateful variants of PKE schemes derived from IBE schemes exist.