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Acquiring accurate labels on large-scale datasets is both time consuming and expensive. To reduce the dependency of deep learning models on learning from clean labeled data, several recent research efforts are focused on learning with noisy labels. These methods typically fall into three design categories to learn a noise robust model: sample selection approaches, noise robust loss functions, or label correction methods. In this paper, we propose PARS: Pseudo-Label Aware Robust Sample Selection, a hybrid approach that combines the best from all three worlds in a joint-training framework to achieve robustness to noisy labels. Specifically, PARS exploits all training samples using both the raw/noisy labels and estimated/refurbished pseudo-labels via self-training, divides samples into an ambiguous and a noisy subset via loss analysis, and designs label-dependent noise-aware loss functions for both sets of filtered labels. Results show that PARS significantly outperforms the state of the art on extensive studies on the noisy CIFAR-10 and CIFAR-100 datasets, particularly on challenging high-noise and low-resource settings. In particular, PARS achieved an absolute 12% improvement in test accuracy on the CIFAR-100 dataset with 90% symmetric label noise, and an absolute 27% improvement in test accuracy when only 1/5 of the noisy labels are available during training as an additional restriction. On a real-world noisy dataset, Clothing1M, PARS achieves competitive results to the state of the art.