Various techniques have been developed and introduced to address the pressing need to create three-dimensional (3D) content for advanced applications such as virtual reality and augmented reality. However, the intricate nature of 3D shapes poses a greater challenge to their representation and generation than standard two-dimensional (2D) image data. Different types of representations have been proposed in the literature, including meshes, voxels and implicit functions. Implicit representations have attracted considerable interest from researchers due to the emergence of the radiance field representation, which allows the simultaneous reconstruction of both geometry and appearance. Subsequent work has successfully linked traditional signed distance fields to implicit representations, and more recently the triplane has offered the possibility of generating radiance fields using 2D content generators. Many articles have been published focusing on these particular areas of research. This paper provides a comprehensive analysis of recent studies on implicit representation-based 3D shape generation, classifying these studies based on the representation and generation architecture employed. The attributes of each representation are examined in detail. Potential avenues for future research in this area are also suggested.