Attackers increasingly use passwords leaked from one website to compromise associated accounts on other websites. Such targeted attacks work because users reuse, or pick similar, passwords for different websites. We recast one of the core technical challenges underlying targeted attacks as the task of modeling similarity of human-chosen passwords. We show how to learn good password similarity models using a compilation of 1.4 billion leaked email, password pairs. Using our trained models of password similarity, we exhibit the most damaging targeted attack to date. Simulations indicate that our attack compromises more than 16% of user accounts in less than a thousand guesses, should one of their other passwords be known to the attacker and despite the use of state-of-the art countermeasures. We show via a case study involving a large university authentication service that the attacks are also effective in practice. We go on to propose the first-ever defense against such targeted attacks, by way of personalized password strength meters (PPSMs). These are password strength meters that can warn users when they are picking passwords that are vulnerable to attacks, including targeted ones that take advantage of the user’s previously compromised passwords. We design and build a PPSM that can be compressed to less than 3 MB, making it easy to deploy in order to accurately estimate the strength of a password against all known guessing attacks.