TThis paper argues that \textbf{a comprehensive vulnerability analysis is essential for building trustworthy Large Language Model-based Multi-Agent Systems (LLM-MAS)}. These systems, which consist of multiple LLM-powered agents working collaboratively, are increasingly deployed in high-stakes applications but face novel security threats due to their complex structures. While single-agent vulnerabilities are well-studied, LLM-MAS introduces unique attack surfaces through inter-agent communication, trust relationships, and tool integration that remain significantly underexplored. We present a systematic framework for vulnerability analysis of LLM-MAS that unifies diverse research. For each type of vulnerability, we define formal threat models grounded in practical attacker capabilities and illustrate them using real-world LLM-MAS applications. This formulation enables rigorous quantification of vulnerability across different architectures and provides a foundation for designing meaningful evaluation benchmarks. We also identify critical open challenges: (1) developing benchmarks specifically tailored to LLM-MAS vulnerability assessment, (2) considering new potential attacks specific to multi-agent architectures, and (3) implementing trust management systems that can enforce security in LLM-MAS. This research provides essential groundwork for future efforts to enhance LLM-MAS trustworthiness.