In this paper, we present "BIKED," a dataset comprised of 4500 individually designed bicycle models sourced from hundreds of designers. We expect BIKED to enable a variety of data-driven design applications for bicycles and support the development of data-driven design methods. The dataset is comprised of a variety of design information including assembly images, component images, numerical design parameters, and class labels. In this paper, we first discuss the processing of the dataset, then highlight some prominent research questions that BIKED can help address. Of these questions, we further explore the following in detail: 1) Are there prominent gaps in the current bicycle market and design space? We explore the design space using unsupervised dimensionality reduction methods. 2) How does one identify the class of a bicycle and what factors play a key role in defining it? We address the bicycle classification task by training a multitude of classifiers using different forms of design data and identifying parameters of particular significance through permutation-based interpretability analysis. 3) How does one synthesize new bicycles using different representation methods? We consider numerous machine learning methods to generate new bicycle models as well as interpolate between and extrapolate from existing models using Variational Autoencoders. The dataset and code are available at http://decode.mit.edu/projects/biked/.