We introduce the notion of public key encryption with secure key leasing (PKE-SKL). Our notion supports the leasing of decryption keys so that a leased key achieves the decryption functionality but comes with the guarantee that if the quantum decryption key returned by a user passes a validity test, then the user has lost the ability to decrypt. Our notion is similar in spirit to the notion of secure software leasing (SSL) introduced by Ananth and La Placa (Eurocrypt 2021) but captures significantly more general adversarial strategies. In more detail, our adversary is not restricted to use an honest evaluation algorithm to run pirated software. Our results can be summarized as follows: 1. Definitions: We introduce the definition of PKE with secure key leasing and formalize security notions. 2. Constructing PKE with Secure Key Leasing: We provide a construction of PKE-SKL by leveraging a PKE scheme that satisfies a new security notion that we call consistent or inconsistent security against key leasing attacks (CoIC-KLA security). We then construct a CoIC-KLA secure PKE scheme using 1-key Ciphertext-Policy Functional Encryption (CPFE) that in turn can be based on any IND-CPA secure PKE scheme. 3. Identity Based Encryption, Attribute Based Encryption and Functional Encryption with Secure Key Leasing: We provide definitions of secure key leasing in the context of advanced encryption schemes such as identity based encryption (IBE), attribute-based encryption (ABE) and functional encryption (FE). Then we provide constructions by combining the above PKE-SKL with standard IBE, ABE and FE schemes.