We address the task of classifying car images at multiple levels of detail, ranging from the top-level car type, down to the specific car make, model, and year. We analyze existing datasets for car classification, and identify the CompCars as an excellent starting point for our task. We show that convolutional neural networks achieve an accuracy above 90% on the finest-level classification task. This high performance, however, is scarcely representative of real-world situations, as it is evaluated on a biased training/test split. In this work, we revisit the CompCars dataset by first defining a new training/test split, which better represents real-world scenarios by setting a more realistic baseline at 61% accuracy on the new test set. We also propagate the existing (but limited) type-level annotation to the entire dataset, and we finally provide a car-tight bounding box for each image, automatically defined through an ad hoc car detector. To evaluate this revisited dataset, we design and implement three different approaches to car classification, two of which exploit the hierarchical nature of car annotations. Our experiments show that higher-level classification in terms of car type positively impacts classification at a finer grain, now reaching 70% accuracy. The achieved performance constitutes a baseline benchmark for future research, and our enriched set of annotations is made available for public download.