Sparse aperture ISAR imaging involves reconstructing high-resolution ISAR images from incomplete echo data.Currently，sparse recovery methods are mainly classified into two kinds of model-driven imaging methods and data-driven imaging methods.This paper first introduces the basic principle of ISAR imaging and the signal model for sparse aperture，then discusses three classes of model-driven compressive sensing methods，namely convex relaxation optimization algorithms，non-convex optimization algorithms，and greedy algorithms，and compares and analyzes the advantages and disadvantages of each method. Subsequently，deep learning-based sparse imaging methods for ISAR are introduced，focusing on neural network based learning and deep unfolding network based learning，with evaluations of their efficacy in ISAR sparse imaging applications.Finally，the content of this paper is summarized and the development trends of sparse aperture ISAR imaging are given.