The active contour model (ACM) approach in image segmentation is regarded as a research hotspot in the area of computer vision, which is widely applied in different kinds of applications in practice, such as medical image processing. The essence of ACM is to make use ofuse an enclosed and smooth curve to signify the target boundary, which is usually accomplished by minimizing the associated energy function by means ofthrough the standard descent method. This paper presents an overview of ACMs for handling image segmentation problems in various fields. It begins with an introduction briefly reviewing different ACMs with their pros and cons. Then, some basic knowledge in of the theory of ACMs is explained, and several popular ACMs in terms of three categories, including region-based ACMs, edge-based ACMs, and hybrid ACMs, are detailedly reviewed with their advantages and disadvantages. After that, twelve ACMs are chosen from the literature to conduct three sets of segmentation experiments to segment different kinds of images, and compare the segmentation efficiency and accuracy with different methods. Next, two deep learning-based algorithms are implemented to segment different types of images to compare segmentation results with several ACMs. Experimental results confirm some useful conclusions about their sharing strengths and weaknesses. Lastly, this paper points out some promising research directions that need to be further studied in the future.