Recommender Systems (RSs) are used to provide users with personalized item recommendations and help them overcome the problem of information overload. Currently, recommendation methods based on deep learning are gaining ground over traditional methods such as matrix factorization due to their ability to represent the complex relationships between users and items and to incorporate additional information. The fact that these data have a graph structure and the greater capability of Graph Neural Networks (GNNs) to learn from these structures has led to their successful incorporation into recommender systems. However, the bias amplification issue needs to be investigated while using these algorithms. Bias results in unfair decisions, which can negatively affect the company reputation and financial status due to societal disappointment and environmental harm. In this paper, we aim to comprehensively study this problem through a literature review and an analysis of the behavior against biases of different GNN-based algorithms compared to state-of-the-art methods. We also intend to explore appropriate solutions to tackle this issue with the least possible impact on the model performance.