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The dominating NLP paradigm of training a strong neural predictor to performone task on a specific dataset has led to state-of-the-art performance in avariety of applications (eg. sentiment classification, span-prediction basedquestion answering or machine translation). However, it builds upon theassumption that the data distribution is stationary, ie. that the data issampled from a fixed distribution both at training and test time. This way oftraining is inconsistent with how we as humans are able to learn from andoperate within a constantly changing stream of information. Moreover, it isill-adapted to real-world use cases where the data distribution is expected toshift over the course of a model's lifetime.  The first goal of this thesis is to characterize the different forms thisshift can take in the context of natural language processing, and proposebenchmarks and evaluation metrics to measure its effect on current deeplearning architectures. We then proceed to take steps to mitigate the effect ofdistributional shift on NLP models. To this end, we develop methods based onparametric reformulations of the distributionally robust optimizationframework. Empirically, we demonstrate that these approaches yield more robustmodels as demonstrated on a selection of realistic problems. In the third andfinal part of this thesis, we explore ways of efficiently adapting existingmodels to new domains or tasks. Our contribution to this topic takesinspiration from information geometry to derive a new gradient update rulewhich alleviate catastrophic forgetting issues during adaptation.

Learning Neural Models for Natural Language Processing in the Face of Distributional Shift