The Vanishing Gradient (VG) problem is a significant challenge during Deep Neural Networks (DNN) training, mainly when using the backpropagation algorithm. This issue is especially true for tasks involving sequential data and long-range dependencies, such as natural language processing (NLP). Over the years, the VG problem has received significant research attention, indicating its importance. However, the few existing studies on the VG problem that offer a subset of work in this area do not provide a structured understanding of the various methods to solve the VG problem. This study briefly explores methods proposed to mitigate the VG problem, categorizing them into three main approaches: (1) modified activation functions, such as ReLU and its variants, which help alleviate gradient shrinkage in deep layers; (2) architectural innovations, such as residual connections and LSTMs, designed to preserve gradient flow over long sequences, and (3) optimization strategies, including advanced methods like Adam, which adapt learning rate dynamically to stabilize training. A comparative analysis of these techniques highlights key insights: while ReLU variants provide simplicity and computational efficiency, they may still struggle with dying neurons; architectural approaches like residual networks offer robust gradient propagation and great potential but at the cost of increased complexity—optimization methods like Adam’s balance computational overhead with improved convergence rates. We conclude by discussing potential future directions for further research in mitigating the vanishing gradient problem, instilling a sense of optimism for the future of deep learning.