As a pivotal strategy to deal with complicated and high-dimensional data, subspace clustering is to find a set of subspaces of a high-dimensional space and then partition each data point in dataset into the corresponding subspace. This field has witnessed remarkable progress over recent decades, with substantial theoretical advancements and successful applications spanning image processing, genomic analysis and text analysis. However, existing surveys predominantly focus on conventional shallow-structured methods, with few up-to-date reviews on deep-structured methods, i.e., deep neural network-based approaches. In fact, recent years has witnessed the overwhelming success of deep neural network in various fields, including computer vision, natural language processing, subspace clustering. To address this gap, this paper presents a comprehensive review on subspace clustering methods, including conventional shallow-structured and deep neural network based approaches, which systematically analyzes over 150 papers published in peer-reviewed journals and conferences, highlighting the latest research achievements, methods, algorithms and applications. Specifically, we first briefly introduce the basic principles and evolution of subspace clustering. Subsequently, we present an overview of research on subspace clustering, dividing the existing works into two categories: shallow subspace clustering and deep subspace clustering, based on the model architecture. Within each category, we introduce a refined taxonomy distinguishing linear and nonlinear approaches based on data characteristics and subspace structural assumptions. Finally, we discuss the challenges currently faced and future research direction for development in the field of subspace clustering.