Large Language Models (LLMs) have revolutionized natural language processing but often rely on outdated information, limiting their relevance and accuracy in real-time applications. Search-augmented LLMs promise to overcome this limitation by integrating real-time search capabilities, potentially transforming internet search and information retrieval. However, challenges such as factual inaccuracies, issues with source attribution, and integration complexities hinder their full potential. This study aims to systematically review existing literature on search-augmented LLMs to understand their current state and identify areas for improvement. We conduct a systematic literature review, categorizing findings into two main streams: evaluation of deployed models and development of new frameworks. Our analysis highlights critical challenges and offers a structured framework for assessing search-augmented LLMs. This contributes to the Information Systems field by informing future research directions and practical applications, ultimately enhancing the effectiveness and reliability of search-augmented LLMs in transforming internet search.