Web accessibility aims to ensure that web content and services are usable by people with diverse abilities. In recent years, Large Language Models (LLMs) have been increasingly explored to support accessibility-related tasks on the web, such as content generation, issue detection, and remediation. However, little is known about the characteristics of these approaches, the accessibility issues they target, the standards they follow, and how they are evaluated. In this paper, we present a systematic literature review of 38 peer-reviewed studies that investigate the use of LLMs in web accessibility contexts. We begin by performing a comprehensive search of scientific publications to identify relevant studies. We then conduct a comparative analysis to examine the accessibility tasks addressed, the LLM models and prompting strategies employed, the system architectures adopted, the accessibility issues and guidelines considered, and the evaluation methods used across studies. Our findings show that most studies apply LLMs to text-centric and structurally explicit accessibility tasks, with WCAG serving as the primary reference framework and limited consideration of cognitive accessibility guidelines (COGA). The reviewed approaches predominantly rely on general-purpose LLMs and prompt-based interactions, while evaluation practices vary widely and often lack direct involvement of users with disabilities. We envision this review as a consolidated reference for researchers and practitioners seeking to understand the current landscape of LLM-supported web accessibility, and as a foundation to guide future research and tool development in this area.