Applications of Large Language Models (LLMs) are rapidly growing in industry and academia for various software engineering (SE) tasks. As these models become more integral to critical processes, ensuring their reliability and trustworthiness becomes essential. Consequently, the concept of trust in these systems is becoming increasingly critical. Well-calibrated trust is important, as excessive trust can lead to security vulnerabilities, and risks, while insufficient trust can hinder innovation. However, the landscape of trust-related concepts in LLMs in SE is relatively unclear, with concepts such as trust, distrust, and trustworthiness lacking clear conceptualizations in the SE community. To bring clarity to the current research status and identify opportunities for future work, we conducted a comprehensive review of $88$ papers: a systematic literature review of $18$ papers focused on LLMs in SE, complemented by an analysis of 70 papers from broader trust literature. Additionally, we conducted a survey study with 25 domain experts to gain insights into practitioners' understanding of trust and identify gaps between existing literature and developers' perceptions. The result of our analysis serves as a roadmap that covers trust-related concepts in LLMs in SE and highlights areas for future exploration.