Modern Automatic Speech Recognition (ASR) technology has evolved to identify the speech spoken by native speakers of a language very well. However, identification of the speech spoken by non-native speakers continues to be a major challenge for it. In this work, we first spell out the key requirements for creating a well-curated database of speech samples in non-native accents for training and testing robust ASR systems. We then introduce AccentDB, one such database that contains samples of 4 Indian-English accents collected by us, and a compilation of samples from 4 native-English, and a metropolitan Indian-English accent. We also present an analysis on separability of the collected accent data. Further, we present several accent classification models and evaluate them thoroughly against human-labelled accent classes. We test the generalization of our classifier models in a variety of setups of seen and unseen data. Finally, we introduce the task of accent neutralization of non-native accents to native accents using autoencoder models with task-specific architectures. Thus, our work aims to aid ASR systems at every stage of development with a database for training, classification models for feature augmentation, and neutralization systems for acoustic transformations of non-native accents of English.