Large language model (LLM)-based chatbots are increasingly integrated into various sectors of people's lives, including education, healthcare, and retail. As they become more ubiquitous, safety concerns have emerged, among them the tendency to ascribe human-like qualities to these systems — a phenomenon known as anthropomorphism. Anthropomorphism can shape not only interpersonal dynamics and affective responses but also foster overreliance and raise privacy concerns. This scoping review synthesizes empirical evidence on the impact of perceived anthropomorphism in LLMs and the system- and user-level factors that modulate this perception. Thematic synthesis revealed that LLM anthropomorphism affects psychological outcomes — including trust, emotional engagement, attachment, and perceptions of competence and warmth — as well as behavioral outcomes such as intention to use and social dynamics. Among system-level factors, conversational style and tone, emotional expressive language, and contextual responsiveness were identified as factors shaping anthropomorphic perception. User-level factors, including loneliness, emotional needs, motivational factors, prior experience with LLMs, as well as individual differences in personality traits, further shaped the degree of perceived anthropomorphism. Although effects were highly context-dependent, anthropomorphism generally enhanced user experience in social or supportive contexts, whereas excessive anthropomorphism sometimes reduced trust or elicited discomfort in formal or task-oriented settings. This review also highlights ongoing methodological challenges and underscores the need for continued research to inform the contextually and ethically sensitive design of LLMs.