Event cameras are rapidly emerging as powerful vision sensors for 3D reconstruction, uniquely capable of asynchronously capturing per-pixel brightness changes. Compared to traditional frame-based cameras, event cameras produce sparse yet temporally dense data streams, enabling robust and accurate 3D reconstruction even under challenging conditions such as high-speed motion, low illumination, and extreme dynamic range. These capabilities offer substantial promise for transformative applications in various fields, including autonomous driving, robotics, aerial navigation, and immersive virtual reality. This survey presents the first comprehensive review exclusively dedicated to event-based 3D reconstruction. Existing approaches are systematically categorized based on input modality as stereo, monocular, or multimodal systems, and further classified according to reconstruction methodologies, including geometry-based techniques, deep learning approaches, and neural rendering techniques such as neural radiance fields (NeRFs) and 3D Gaussian splatting (3DGS). Within each category, methods are chronologically organized to highlight the evolution of key concepts and advances. We also provide a detailed summary of publicly available datasets specifically suited to event-based reconstruction tasks. Finally, we discuss significant open challenges in dataset availability, standardized evaluation, effective representation, and dynamic scene reconstruction, suggesting directions for future research. This survey aims to serve as a reference and to provide a clear and motivating roadmap for advancing the state-of-the-art in event-driven 3D reconstruction.