With the advancement of web techniques, they have significantly revolutionized various aspects of people’s lives. Despite the importance of the web, many tasks performed on it are repetitive and time-consuming, negatively impacting overall quality of life. To efficiently handle these tedious daily tasks, one of the most promising approaches is to advance autonomous agents based on Artificial Intelligence (AI) techniques, referred to as AI Agents, as they can operate continuously without fatigue or performance degradation. In the context of the web, leveraging AI Agents – termed WebAgents – to automatically assist people in handling tedious daily tasks can dramatically enhance productivity and efficiency. Recently, Large Foundation Models (LFMs) containing billions of parameters have exhibited human-like language understanding and reasoning capabilities, showing proficiency in performing various complex tasks. This naturally raises the question: `Can LFMs be utilized to develop powerful AI Agents that automatically handle web tasks, providing significant convenience to users?’ To fully explore the potential of LFMs, extensive research has emerged on WebAgents designed to complete daily web tasks according to user instructions, significantly enhancing the convenience of daily human life. In this survey, we comprehensively review existing research studies on WebAgents across three key aspects: architectures, training, and trustworthiness. Additionally, several promising directions for future research are explored to provide deeper insights.