This article proposes a topic modeling method that scales linearly to billions of documents. We make three core contributions: i) we present a topic modeling method, tensor latent Dirichlet allocation, that has identifiable and recoverable parameter guarantees and sample complexity guarantees for large data; ii) we show that this method is computationally and memory efficient (achieving speeds over 3$\times $–4$\times $ those of prior parallelized latent Dirichlet allocation methods), and that it scales linearly to text datasets with over a billion documents; and iii) we provide an open-source, GPU-based implementation of this method. This scaling enables previously prohibitive analyses, and we perform two real-world, large-scale new studies of interest to political scientists: we provide the first thorough analysis of the evolution of the #MeToo movement through the lens of over two years of Twitter conversation and a detailed study of social media conversations about election fraud in the 2020 presidential election. Thus, this method provides social scientists with the ability to study very large corpora at scale and to answer important theoretically-relevant questions about salient issues in near real-time.