This review article provides a comparative analysis of communicative convergence in written dialogues between humans and Large Language Models (LLMs). It draws on theoretical work on communication accommodation and interactive alignment as well as empirical research on linguistic adaptation in human–computer and human–LLM interaction. The reviewed studies address lexical, syntactic, stylistic, pragmatic, and ideological alignment, together with the effects of prompt wording and dialogue history on model responses. The comparison shows that similar manifestations of convergence arise from different mechanisms: in humans, they may reflect affiliation, priming, and interactional coordination, whereas in LLMs they result from probabilistic text generation and sensitivity to context. Convergence is bidirectional but asymmetrical: users adapt their language to the perceived characteristics and constraints of the system, while models reproduce or amplify cues present in user input. Apparent alignment should not be treated as evidence of communicative intention or shared understanding. Instead, human–LLM convergence is best understood as an interactional effect jointly produced by human social-cognitive mechanisms and the model’s contextual responsiveness. The review also identifies a shortage of longitudinal research and studies involving morphologically rich languages, including Polish.