PT/hreshold public-key cryptography/ allows to distribute the power to execute a private operation (decryption or signature) among a pool of players: if a given threshold of authorized players cooperate the operation is possible. In this talk, I will review this setting and especially for encryption, and extend it to the dynamic case, where any user can /dynamically /join the system, as a possible recipient; the sender can /dynamically /choose the authorized set of recipients, for each ciphertext; and the sender can /dynamically/ set the threshold /t/ for decryption capability among the authorized set. I will first present a formal security model, which includes strong robustness notions, and then propose a candidate achieving all the above dynamic properties, that is semantically secure in the standard model, under a new non-interactive assumption, that fits into the general Diffie-Hellman exponent framework on groups with a bilinear map. It furthermore compares favorably with previous proposals, /a.k.a./ threshold broadcast encryption, since this is the first threshold public-key encryption, with dynamic authorized set of recipients and dynamic threshold that provides constant-size ciphertexts. This is a joint work with Cécile Delerablée.