Over the last decade, linear models have become the standard machine learning approach for supervised classification, ranking, and structured prediction natural language processing. They can handle very high-dimensional problem representations, they are easy to set up and use, and they extend naturally to complex structured problems. But there is something unsatisfying in this work. The geometric intuitions behind linear models were developed with low-dimensional, continuous problems, while natural language problems involve very high dimension, discrete representations with long tailed distributions. Do the orignal intuitions carry over? In particular, do standard regularization methods make any sense for language problems? I will give recent experimental evidence that there is much to do in making linear model learning more suited to the statistics of language.