This paper provides a systematic survey of artificial intelligence (AI) models that have been proposed over the past decade to screen retinal diseases, which can cause severe visual impairments or even blindness. The paper covers both the clinical and technical perspectives of using AI models in hosipitals to aid ophthalmologists in promptly identifying retinal diseases in their early stages. Moreover, this paper also evaluates various methods for identifying structural abnormalities and diagnosing retinal diseases, and it identifies future research directions based on a critical analysis of the existing literature. This comprehensive study, which reviews both the conventional and state-of-the-art methods to screen retinopathy across different modalities, is unique in its scope. Additionally, this paper serves as a helpful guide for researchers who want to work in the field of retinal image analysis in the future.