The distractor generation task focuses on generating incorrect but plausible options for objective questions such as fill-in-the-blank and multiple-choice questions. This task is widely utilized in educational settings across various domains and subjects. The effectiveness of these questions in assessments relies on the quality of the distractors, as they challenge examinees to select the correct answer from a set of misleading options. The evolution of artificial intelligence (AI) has transitioned the task from traditional methods to the use of neural networks and pre-trained language models. This shift has established new benchmarks and expanded the use of advanced deep learning methods in generating distractors. This survey explores distractor generation tasks, datasets, methods, and current evaluation metrics for English objective questions, covering both text-based and multi-modal domains. It also evaluates existing AI models and benchmarks and discusses potential future research directions.