The ever pervasive growth in information services and technology has resulted in the outbreak of demand for data in the wireless networks. This has made the network operators to ponder over the imminent difficulties, such as computing capabilities and fronthaul–backhaul link capacities. Hence, to bridge the gap between the cloud capacity and requirement of mobile services by the network edges, edge computing, and caching techniques have been gaining more and more attention from researchers across the world. Further, motivated by the successful applications of machine learning (ML) in solving complex and dynamic problems, in this article, it has been used to advance edge caching capabilities. The proposed ML-based algorithms have been evaluated and proved to have better performance compared with the existing conventional algorithms. The mean squared error (mse), for the proposed deep learning (DL) algorithm, is 20-times less than the existing algorithms and while comparing with the simple neural network, the gain in mse for the proposed DL algorithm is observed around 27%. Similarly for the federated learning-based caching algorithm, the average cache hit gain is of the order of $10^{4}$, hence demonstrating the benefit of the proposed algorithms. In addition, opportunities and challenges for a promising upcoming future of ML in edge computing and content popularity prediction have also been discussed.