The optic disc and optic cup segmentation techniques are used to isolate the relevant parts of the retinal image and to calculate the cup-to-disc ratio. The main objective of this paper is to review segmentation methodologies and techniques for the disc and cup boundaries which are utilized to calculate the disc and cup geometrical parameters automatically and accurately to help the professionals in the glaucoma to have a wide view and more details about the optic nerve head structure using retinal fundus images. We provide a brief description of each technique, highlighting its classification and performance metrics. The current and future research directions are summarized and discussed. We present several state-of-the-art procedures to extract the anatomic components and lesions in color fundus photographs and decision support methods to help clinical diagnosis. We list publicly available databases and appropriate measurement techniques to compare quantitatively the performance of these approaches. Furthermore, we discuss on how the performance of image processing-based systems can be improved by fusing the output of individual detector algorithms. Retinal image analysis using mobile phones is also addressed as an expected future trend in this field.