An increasing availability of remote sensing data in the era of geo big-data makes producing well-represented, reliable training data to be more challenging and requires an excessive amount of human labor. In addition, the rapid increase in graphics processing unit (GPU) processing power has enabled the development of advanced deep learning (DL) algorithms, which achieve impressive results in the field of satellite image processing. However, they require a huge and comprehensive training dataset to avoid overfitting problems and to represent a generalizable model. Thus, moving toward the development of non-supervised deep learning (NSDL) models in different remote sensing applications is an inevitable need. To provide an initial response to that need, this paper performs a comprehensive review and systematic meta-analysis of recently published research articles focusing on the applications of NSDL for remote sensing data processing. In order to identify future research directions and formulate recommendations, we extract trends and highlight interesting approaches from this large body of literature. Consequently, current challenges, prospects, and recommendations are also discussed to uncover the trend. According to the results, there is a sharp increasing trend in the applicability of NSDL methods during these few years particularly, with the advent of new deep architectures, such as adversarial, graph, and transformer models. As a result, this review paper discusses different remote sensing data processing applications and challenges that can be addressed using NSDL approaches.