"Classification" is an important topic in data mining. The task is to induce---using only data examples---a model of the database which will let us predict any new object's type based on its other features. We have an interesting tension here: on the one hand, we want accurate predictions; on the other, we want to be able to explain the results in terms of the features. Furthermore, we want the process to be scalable and automatic. Decision trees and artificial neural networks each represent a trade-off in this tension. Decision trees are scalable and can provide us with "rules" to explain why each prediction is made. Unfortunately some prediction accuracy is sacrificed to the simplicity of the model. Neural networks often provide better accuracy, at the cost of somewhat poor scalability and mysterious reasons for their behaviour. In this talk, I will introduce the topic of "transformational hybrid systems" and show how this idea may help us to harness the best of both methods. After outlining some of the relevant techniques already studied in this area, I'll present some preliminary results of a successful tree-to-network mapping. Finally, I will outline some ideas for where this research might go next.