Histograms of local appearance descriptors are a popular representation for visual recognition. They are highly discriminant and they have good resistance to local occlusions and to geometric and photometric variations, but they are not able to exploit spatial co-occurrence statistics of features at scales larger than their local input patches. We present a new multilevel visual representation, `hyperfeatures', that is designed to remedy this. The basis of the work is the familiar notion that to detect object parts, in practice it often suffices to detect co-occurrences of more local object fragments a process that can be formalized as comparison (vector quantization) of image patches against a codebook of known fragments, followed by local aggregation of the resulting codebook membership vectors to detect co-occurrences. This process converts collections of local image descriptor vectors into slightly less local histogram vectors higher-level but spatially coarser descriptors. Our central observation is that it can therefore be iterated, and that doing so captures and codes ever larger assemblies of object parts and increasingly abstract or `semantic' image properties. This repeated nonlinear `folding' is essentially different from that of hierarchical models such as Convolutional Neural Networks and HMAX, being based on repeated comparison to local prototypes and accumulation of co-occurrence statistics rather than on repeated convolution and rectification. We formulate the hyperfeatures model and study its performance under several different image coding methods including clustering based Vector Quantization, Gaussian Mixtures, and combinations of these with Latent Discriminant Analysis. We find that the resulting high-level features provide improved performance in several object image and texture image classification tasks.