Kidney stones are hard deposits that form due to an accumulation of minerals and other materials in the kidneys. Early detection of kidney stones is crucial to avoid complications, provide efficient treatment and enhance the quality of life for patients. A number of diagnostic methods, consisting in imaging and laboratory measures, is employed to detect these stones. In recent times, with the advent of machine learning (ML) and deep learning (DL), there has been impressive progress in identification of kidney stones from radiological images like CT, X-ray and MRI. These models will not only help to detect stones but also estimate their size and location in 3D anatomical space. The detection and characterization of kidney stones is a common problem in multimodal imaging where each imaging modality provides different aspects of stone information. In recent years there has been a proliferation of ML and DL based approaches to address this problem. We provide a complete overview of the popular MLs and DLs used for detecting kidney stones in radiographic imaging within this review.