The project is situated at the intersection of computer science and cognitive psychology with philosophy of mind and clinical psychology as supporting fields. This project asks what cognitive competencies LLMs can acquire through language mastery, how robust these competencies are, and how they diverge from their human counterparts. It investigates two themes: internal representations of the world, understood as situation modelling, and internal representations of self, understood as introspective access. The first theme examines whether LLMs construct and update situation models, tracking entities, properties and relations across discourse, in ways that parallel human cognition or rely on different computational strategies. The second examines whether LLM introspection is better characterised by inference-based or direct-access accounts, and how it compares to human performance on matched behavioural paradigms. A central contribution of this project is methodological: novel experimental paradigms will be developed with cognitive psychologists and psycholinguists to establish robust, replicable human baselines, which existing LLM evaluations lack. State-of-the-art models will then be tested under matched conditions, with comparisons across model families isolating factors such as scale and instruction tuning. Behavioural divergences will be systematically characterised into a taxonomy of failure modes and traced to their computational causes using mechanistic interpretability. Finally, findings from both themes will be synthesised into concrete recommendations for improving model calibration in safety-critical and clinical contexts.