Large language models have recently achieved state of the art performance across a wide variety of natural language tasks. Meanwhile, the size of these models and their latency have significantly increased, which makes their usage costly, and raises an interesting question: do language models need to be large? We study this question through the lens of model compression. We present a generic, structured pruning approach by parameterizing each weight matrix using its low-rank factorization, and adaptively removing rank-1 components during training. On language modeling tasks, our structured approach outperforms other unstructured and block-structured pruning baselines at various compression levels, while achieving significant speedups during both training and inference. We also demonstrate that our method can be applied to pruning adaptive word embeddings in large language models, and to pruning the BERT model on several downstream fine-tuning classification benchmarks.