Edge and contour detection plays critical roles in computer vision and image processing, with extensive applications in advanced tasks including object recognition, shape matching, visual saliency, image segmentation, and inpainting. In recent decades, this field has attracted significant attention, leading to the development of numerous sophisticated methods that approximate human visual performance. Despite these advances, notable gaps remain. This review offers a comprehensive analysis of representative techniques, categorizing them into traditional and learning-based approaches, and examines their strengths and limitations to identify the underlying reasons for these gaps. Traditional methods are further divided into four sub-categories: local pattern, edge grouping, active contour, and bio-inspired techniques, with a specific emphasis on the promising potential of bio-inspired methods. Learning-based approaches, on the other hand, are classified into two types: classical learning, which typically relies on handcrafted features designed from empirical knowledge, and deep learning, which autonomously extracts features from large-scale datasets without human intervention. Additionally, benchmarks and evaluation metrics related to edge and contour detection are discussed, with potential issues identified within these frameworks. A quantitative assessment of representative methods is conducted across three popular benchmarks. Lastly, challenges and future prospects in edge and contour detection are explored, focusing on five key aspects: model architecture, learning strategies, feature extraction and fusion, method integration, and cross-domain applications. These considerations aim to bridge the gap with human visual perception. Overall, this work is expected to benefit researchers and advance progress in the field.