To the extent that such models are trained to predict the properties of specific molecules or materials, they belong to the standard class of inductive supervised learning. However, many groups have been exploring ways of instead specifying the properties (or set of properties) as a model input to predict molecules or materials that match those specifications. This learning task has been popularized as the "inverse problem", since it is the inverse of the typical inductive learning task, and the resulting models are known as "generative" because they have the ability to generate samples that would ordinarily be in input to a supervised learning task. Such models have tremendous theoretical appeal, with the ultimate vision being that a researcher punches in a set of properties and the model returns a chemical structure matching those criteria (and potentially even instructions for an automated synthesizer to make a batch). Unfortunately, the current state-of-the-art is very far from matching this vision. Practical solutions to the inverse problem are to solve the forward problem many times on either a tractable chemical subspace or using an objective function to guide the search over candidates (e.g., using a genetic algorithm). Alternatively, architectures like autoencoders and adversarial networks provide generative capabilities as a byproduct of otherwise standard supervised training. A major deficiency of these models is that it isn't obvious how to systematically improve them, since their training currently relies on regularization heuristics and inductive bias(es) to shift the distribution of generated chemistries into more useful regions. We have included inverse design here as an example of a deductive problem with insufficiently informative input features. The input features, typically one or more properties like a bandgap, are manifestly insufficient to uniquely determine a molecular structure. Nevertheless, this does not stop an expert from designing a molecule or polymer with a target bandgap. This is because xvi the expert approaches the task deductively by restricting the search space based on experience.