Many important advances of deep learning techniques have originated from the efforts of addressing the image classification task on large-scale datasets. However, the construction of clean datasets is costly and time-consuming since the Internet is overwhelmed by noisy images with inadequate and inaccurate tags. In this paper, we propose a Ubiquitous Reweighting Network (URNet) that can learn an image classification model from noisy web data. By observing the web data, we find that there are five key challenges, i.e., imbalanced class sizes, high intra-classes diversity and inter-class similarity, imprecise instances, insufficient representative instances, and ambiguous class labels. With these challenges in mind, we assume every training instance has the potential to contribute positively by alleviating the data bias and noise via reweighting the influence of each instance according to different class sizes, large instance clusters, its confidence, small instance bags, and the labels. In this manner, the influence of bias and noise in the data can be gradually alleviated, leading to the steadily improving performance of URNet. Experimental results in the WebVision 2018 challenge with 16 million noisy training images from 5000 classes show that our approach outperforms state-of-the-art models and ranks first place in the image classification task.