The autocorrelation is often used in signal processing as a tool for finding repeating patterns in a signal. In image processing, there are various image analysis techniques that use the autocorrelation of an image in a broad range of applications from texture analysis to grain density estimation. This paper provides an extensive review of two recently introduced and related frameworks for image representation based on autocorrelation, namely Patch Autocorrelation Features (PAF) and Translation and Rotation Invariant Patch Autocorrelation Features (TRIPAF). The PAF approach stores a set of features obtained by comparing pairs of patches from an image. More precisely, each feature is the euclidean distance between a particular pair of patches. The proposed approach is successfully evaluated in a series of handwritten digit recognition experiments on the popular MNIST data set. However, the PAF approach has limited applications, because it is not invariant to affine transformations. More recently, the PAF approach was extended to become invariant to image transformations, including (but not limited to) translation and rotation changes. In the TRIPAF framework, several features are extracted from each image patch. Based on these features, a vector of similarity values is computed between each pair of patches. Then, the similarity vectors are clustered together such that the spatial offset between the patches of each pair is roughly the same. Finally, the mean and the standard deviation of each similarity value are computed for each group of similarity vectors. These statistics are concatenated to obtain the TRIPAF feature vector. The TRIPAF vector essentially records information about the repeating patterns within an image at various spatial offsets. After presenting the two approaches, several optical character recognition and texture classification experiments are conducted to evaluate the two approaches. Results are reported on the MNIST (98.93%), the Brodatz (96.51%), and the UIUCTex (98.31%) data sets. Both PAF and TRIPAF are fast to compute and produce compact representations in practice, while reaching accuracy levels similar to other state-of-the-art methods.