The optical representation of the eye’s internal processes is provided by retinal fundus image. Various factors causing visual impairments like Glaucoma, Diabetic retinopathy, cataract, corneal opacity, trachoma etc. can be diagnosed by analyzing the retinal fundus images. Segmentation of salient regions and classification are two important functionalities in the analysis of retinal fundus images. Various methods have been proposed with various degree of effectiveness for segmentation and classification. Recently many deep learning techniques with various innovations in terms of network structure, learning mode, hyper parameter optimizations etc. are proposed for improving the effectiveness of the two important functionalities. This work does a critical analysis of existing hybrid deep learning techniques for retinal fundus image segmentation and classification. The objective is to identify open issues and research gaps in two categories of retinal fundus image segmentation and classification. Based on identified open issues, possible solutions to solve the open issues are identified for both functionalities of segmentation and classification.