Autonomous vehicles have emerged as a transformative technology with wide-ranging implications for smart cities, revolutionizing transportation systems and optimizing urban mobility. Object detection plays a crucial role in autonomous vehicles, accurately identifying and localizing pedestrians, vehicles, and traffic signs for safe navigation. Deep learning-based approaches have revolutionized object detection, leveraging deep neural networks to extract intricate features from visual data, enabling superior performance in various domains. Two-stage algorithms like R-FCN and Mask R-CNN focus on precise object localization and instance-level segmentation, while one-stage algorithms like SSD, RetinaNet, and YOLO offer real-time performance through single-pass processing. To advance object detection for autonomous vehicles, comprehensive studies are needed, particularly on two-stage and one-stage algorithms. This study aims to conduct an in-depth analysis, evaluating the strengths, limitations, and performance of R-FCN, Mask R-CNN, SSD, RetinaNet, and YOLO algorithms in the context of autonomous vehicles and smart cities. The research contributions include a thorough analysis of two-stage algorithms, a comprehensive examination of one-stage algorithms, and a comparison of different YOLO variants to highlight their advantages and drawbacks in object detection tasks.