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The rapid integration of artificial intelligence (AI) into materials science has transformed workflows for property prediction, inverse design, and autonomous experimentation. Yet, it has simultaneously introduced profound challenges regarding when and how human researchers should trust AI-generated recommendations in high-stakes contexts. This review systematically examines conceptual models of trust in materials AI by synthesizing interdisciplinary insights from human factors engineering, psychology, and human-computer interaction with domain-specific literature on automated materials discovery. A targeted literature search across Web of Science, Scopus, arXiv, and the ACM Digital Library, employing search strings focused on trust in AI systems, trust calibration, trustworthiness, and human-AI interaction in scientific discovery, yielded approximately 450 initial records. After applying inclusion criteria limited to peer-reviewed English-language publications from 2017 to 2024 that addressed conceptual foundations, frameworks, or applications of trust in AI (with explicit relevance to scientific or materials contexts), 30 studies were selected for in-depth analysis following a PRISMA-style screening process. Conceptual foundations of trust are reviewed, drawing on foundational definitions that position trust as an attitude that an agent will help achieve goals under conditions of uncertainty and vulnerability, while distinguishing it from mere reliance and emphasizing the necessity of calibration for appropriate reliance levels. Existing frameworks for trust in AI are surveyed, revealing recurring components such as competence, integrity, benevolence, performance, process, and purpose, each evaluated for strengths and limitations when transposed to materials AI environments characterized by black-box models, rare events, and high economic or safety stakes. The current state of trust research in materials AI demonstrates a pronounced gap: the majority of studies prioritize predictive accuracy and scalability, with only emergent attention to trustworthiness, explainability, or human trust dynamics. Dimensions of trust tailored to materials AI—predictive competence, uncertainty calibration, transparency, robustness, benevolence, and accountability—are proposed and analyzed in relation to domain-specific challenges. This review articulates open questions surrounding trust establishment, post-failure dynamics, and stakeholder variations while offering recommendations for trust-aware design, evaluation, and reporting. By bridging broader AI trust literature with materials science realities, the work advocates for a paradigm shift from accuracy-centric evaluation toward integrated trust models that ensure safe, effective, and ethically sound human-AI collaboration in materials discovery and innovation.