Sequences arise in many online and offline settings: urls to visit, songs to listen to, videos to watch, restaurants to dine at, and so on. User-generated sequences are tightly related to mechanisms of choice, where a user must select one from a finite set of alternatives. In this talk, we will survey a class of problems arising from studying such sequences and the role discrete choice theory plays in these problems. We will present modeling and algorithmic approaches to some of these problems and illustrate them in the context of large-scale data analysis. This survey is based on work that appeared in (Ashton et al., 2014; Austin et al., 2016; Kumar et al., 2017; Kumar et al., 2015)