Neural Audio Synthesis is dedicated to generating sound through generative neural networks. Sound effects are defined as auditory elements that complement a specific scene (in cinema, fiction, or videogames), support a storyline, enhance a fictional environment, or improve the perceived plausibility and presence (including Virtual Reality) without being music or dialog. This manuscript presents a quantitative literature review of the literature that intersects these two domains: the neural generation of sound effects. By leveraging large language models, we performed an extensive and systematic survey of the major scientific repositories, filtering the most relevant articles to ensure a thorough analysis. Our study examines various generation paradigms employed in sound synthesis, the specific types of sound effects created, the datasets used, and the evaluation metrics considered. Furthermore, we provide a forward-looking discussion on the evolution of this field towards multimodal approaches, where sound generation might integrate with other sensory modalities. All supporting materials and code are available online.