The seminal work of Gatys et al. demonstrated the power of Convolutional Neural Networks (CNNs) in creating artistic imagery by separating and recombining image content and style. This process of using CNNs to render a content image in different styles is referred to as Neural Style Transfer (NST). Since then, NST has become a trending topic both in academic literature and industrial applications. It is receiving increasing attention and a variety of approaches are proposed to either improve or extend the original NST algorithm. In this paper, we aim to provide a comprehensive overview of the current progress towards NST. We first propose a taxonomy of current algorithms in the field of NST. Then, we present several evaluation methods and compare different NST algorithms both qualitatively and quantitatively. The review concludes with a discussion of various applications of NST and open problems for future research. A list of papers discussed in this review, corresponding codes, pre-trained models and more comparison results are publicly available at: https://osf.io/f8tu4/.