Emerging non-volatile memory (NVM) technologies promise the durability of disks with the performance of volatile memory (RAM). To describe the persistency guarantees of NVM, several memory persistency models have been proposed. However, the persistency semantics of the ubiquitous x86 architecture remains unexplored to date. To close this gap, we develop the Px86 (‘persistent x86’) model, formalising the persistency semantics of x86 for the first time. We formulate Px86 both operationally and declaratively, and prove that the two characterisations are equivalent. To demonstrate the application of Px86 and to make persistent programming accessible to the uninitiated programmer, we develop two persistent libraries over Px86: a persistent transactional library, and a persistent variant of the Michael-Scott queue library. We further showcase the application of Px86 by encoding it in Alloy and generating persistency litmus tests automatically.