Prevalent federated learning commonly develops under the assumption that the ideal global class distributions are balanced. In contrast, real-world data typically follows the long-tailed class distribution, where models struggle to classify samples from tail classes. In this paper, we alleviate the issue under the long-tailed data, dissecting the into two aspects: the distorted feature space and the biased classifier. Specifically, we propose the Representation Unification and Classifier Rectification (RUCR), which leverages global unified prototypes to shape the feature space and calibrate the classifier. RUCR aggregates local prototypes (class-wise mean features) extracted by the global model to obtain global unified prototypes. It calibrates the feature space by pulling features within the same class towards corresponding global unified prototypes and pushing the other classes away. Moreover, RUCR utilizes global prototypes to reduce the classifier bias via prototypical mix-up. It generates a balanced virtual feature set by arbitrarily fusing global unified prototypes and local features. The classifier re-training is then conducted on the balanced virtual feature set to rectify the decision boundary and thus alleviate the shifts. Empirical results on CIFAR-10-LT, CIFAR-100-LT, and Tiny-Imagenet-LT datasets validate the superior performance of our proposed method.