Do deep learning models learn human-like representations? If not, could we align their representations with human knowledge to improve performance? In this talk, I will describe a key difference in human and model representations: model representations capture local semantic relationships accurately, but do not accurately capture the global structure of human semantic representations. I will therefore describe a simple method for aligning the global structure of model representations with human knowledge, while preserving their accurate local structure. This alignment dramatically improves agreement with human judgments on a range of cognitive tasks, makes model uncertainty match human answer distributions more closely, and improves downstream performance on machine learning tasks like anomaly detection and few-shot learning. I will close by reflecting on the broader implications and promise of these results.