In this survey, we present a detailed examination of the advancements in Neural Question Generation (NQG), a field leveraging neural network techniques to generate relevant questions from diverse inputs like knowledge bases, texts, and images. The survey begins with an overview of NQG's background, encompassing the task's problem formulation, prevalent benchmark datasets, established evaluation metrics, and notable applications. It then methodically classifies NQG approaches into three predominant categories: structured NQG, which utilizes organized data sources, unstructured NQG, focusing on more loosely structured inputs like texts or visual content, and hybrid NQG, drawing on diverse input modalities. This classification is followed by an in-depth analysis of the distinct neural network models tailored for each category, discussing their inherent strengths and potential limitations. The survey culminates with a forward-looking perspective on the trajectory of NQG, identifying emergent research trends and prospective developmental paths. Accompanying this survey is a curated collection of related research papers, datasets and codes, systematically organized on Github, providing an extensive reference for those delving into NQG.