3D modeling is increasingly pervasive in many industries to produce a 3D digital representation of any object. Nonetheless, traditional 3D modeling remains a laborious and expensive undertaking, requiring a high degree of expertise and patience to create realistic models. GANs have shown great promise in the application of 3D object reconstruction and there has been a vast amount of research being conducted on this topic in recent years. However, given the many potential fields of application for GANs, little work has been produced on the study of current state-of-the-art methods and what kind of future uses they may have. In this paper, we present a systematic literature review of the current unsupervised and weakly-supervised methods on volumetric 3D object reconstruction utilizing GANs with a voxel representation. The review aims at offering insights into future works based on the constraints and potentials of the studied works.