We describe the state of our work on Prediction Games for unsupervised cumulative learning of structured perceptual concepts. Here, concepts predict one another and are built from each other. Improving at prediction drives the learning, and co-occurrences drive concept construction. In each episode, through the process of interpretation, the system determines which of its many concepts are useful, i.e.  form a coherent account of (low-level) buffer contents. By practicing many interpretations, prediction weights are continually updated, and from time to time new concepts are generated, leading to improved predictions and more coherent accounting. Over the past few years, our approach has become more probabilistic and information-theoretic. We report on our improved results in recovering good split (e.g.  word) boundaries, when starting at character or lower levels. We describe our current understanding of the challenges, including internal and external non-stationarity, and incorporating new concepts, as well as potential applications.