Autonomous vehicles are gaining popularity, and the development of automatic parking systems is a fundamental requirement. Detecting the parking slots accurately is the first step towards achieving an automatic parking system. However, modern parking slots present various challenges for detection task due to their different shapes, colors, functionalities, and the influence of factors like lighting and obstacles. In this comprehensive review paper, we explore the realm of vision-based deep learning methods for parking slot detection. We categorize these methods into four main categories: object detection, image segmentation, regression, and graph neural network, and provide detailed explanations and insights into the unique features and strengths of each category. Additionally, we analyze the performance of these methods using three widely used datasets: the Tongji Parking-slot Dataset 2.0 (ps 2.0), Sejong National University (SNU) dataset, and panoramic surround view (PSV) dataset, which have played a crucial role in assessing advancements in parking slot detection. Finally, we summarize the findings of each method and outline future research directions in this field.