Large language models (LLMS) emerge as the most promising Natural Language Processing approach for clinical practice acceleration (i.e., diagnosis, prevention and treatment procedures). Similarly, intelligent conversational systems that leverage LLMS have disruptively become the future of therapy in the era of ChatGPT. Accordingly, this research addresses the application of LLMS in healthcare, paying particular attention to two relevant use cases: cognitive decline and depression, more specifically, postpartum depression. In the end, the most promising opportunities they represent (e.g., clinical tasks augmentation, personalized healthcare, etc.) and related concerns (e.g., data privacy and quality, fairness, etc.) are discussed to contribute to the global debate on their integration in the sanitary system.