Traditional statistical tools and methods are designed to allow inference (with confidence) about a population from a small sample.  While this style of statistics will always have a place, it is now the case that one often can access so much data that using a strictly parametric model can be limiting.  This talk will touch on a Bayesian nonparametric approach to learning models of discrete sequences, an approach which allows us to embrace the flood of data while still preserving a role for a parametric model.    Due to both model complexity and data volume, computational considerations arise quickly in Bayesian nonparametrics.  We will show how, in one case, a careful marriage of probability and algorithmic theory gives rise to a practical, unsupervised, life-long, incremental learning algorithm called the sequence memoizer that can be used as a drop-in replacement for finite-order Markov models.  We will demonstrate the sequence memoizer in two applications, language modeling and general purpose lossless compression.