Abstract: 3D reconstruction method based on computer vision is widely used in various industries. Though the 3D reconstruction of opaque surfaces with Lambertian reflectance on which the current research is mainly concentrated is a well-studied issue, the non-Lambertian surfaces pose challenging problems for the 3D reconstruction. Unfortunately, most surfaces of the objects in the actual scene are non-Lambertian, therefore, a growing body of recent work has concentrated on the real-world problems, and has been concerned primarily with non-Lambertian surfaces reconstruction from images in the field of computer vision. Although this state of the art report does not cover exhaustively the generic methods of 3D reconstruction for non-Lambertian surfaces, it does contain examples of all the significantly different approaches to the steps in this field. The works discussed in the survey are categorized and reviewed in order. The main categories of classification are defined in terms of the illumination used for capturing the image and the principle based on. Due to lack of the common test bench available on the web and stereo data sets of non-Lambertian surfaces with ground truth, it is difficult to compare the computational efficiency and matching quality of the various schemes. In that case, here we are concerned with only the principle and characteristics of the existing methods, the scope of application and the latest trends in the research. We conclude the survey by discussing open problems and future perspectives and hope to provide an entry point to this existing field.