Convolutional neural networks (CNNs) for multi-class classification require training on large, representative, and high quality annotated datasets. However, in the field of medical imaging, data and annotations are both difficult and expensive to acquire. Moreover, they frequently suffer from highly imbalanced distributions, and potentially noisy labels due to intra- or inter-expert disagreement. To deal with such challenges, we propose a unified curriculum learning framework to schedule the order and pace of the training samples presented to the optimizer. Our novel framework reunites three strategies consisting of individually weighting training samples, reordering the training set, or sampling subsets of data. The core of these strategies is a scoring function ranking the training samples according to either difficulty or uncertainty. We define the scoring function from domain-specific prior knowledge or by directly measuring the uncertainty in the predictions. We perform a variety of experiments with a clinical dataset for the multi-class classification of proximal femur fractures and the publicly available MNIST dataset. Our results show that the sequence and weight of the training samples play an important role in the optimization process of CNNs. Proximal femur fracture classification is improved up to the performance of experienced trauma surgeons. We further demonstrate the benefits of our unified curriculum learning method for three controlled and challenging digit recognition scenarios: with limited amounts of data, under class-imbalance, and in the presence of label noise.