Diabetic retinopathy, which is extreme visual blindness due to diabetes, has become an alarming issue worldwide. Early and accurate detection of DR is necessary to prevent the progression and reduce the risk of blindness. Recently, many approaches for DR detection have been proposed in the literature. Among them, deep neural networks (DNNs), especially Convolutional Neural Network (CNN) models, have become the most offered approach. However, designing and training new CNN architectures from scratch is a troublesome and labor-intensive task, particularly for medical images. Moreover, it requires training tremendous amounts of parameters. Therefore, transfer learning approaches as pre-trained models have become more prevalent in the last few years. Accordingly, in this study, 43 publications based on DNN and Transfer Learning approaches for DR detection between 2016 and 2021 are reviewed. The reviewed papers are summarized in 4 figures and 10 tables that present detailed information about 29 pre-trained CNN models, 13 DR data sets, and standard performance metrics.