Estimation of ideological positions among voters, legislators, and other actors is central to many subfields of political science. Recent applications include large data sets of various types including roll calls, surveys, and textual and social media data. To overcome the resulting computational challenges, we propose fast estimation methods for ideal points with massive data. We derive the expectation-maximization (EM) algorithms to estimate the standard ideal point model with binary, ordinal, and continuous outcome variables. We then extend this methodology to dynamic and hierarchical ideal point models by developing variational EM algorithms for approximate inference. We demonstrate the computational efficiency and scalability of our methodology through a variety of real and simulated data. In cases where a standard Markov chain Monte Carlo algorithm would require several days to compute ideal points, the proposed algorithm can produce essentially identical estimates within minutes. Open-source software is available for implementing the proposed methods.