Medical text, as part of an electronic health record, is an essential information source in healthcare. Although natural language processing (NLP) techniques for medical text are developing fast, successful transfer into clinical practice has been rare. Especially the hospital domain offers great potential while facing several challenges including many documents per patient, multiple departments and complex interrelated processes. In this work, we survey relevant literature to identify and classify approaches which exploit NLP in the clinical context. Our contribution involves a systematic mapping of related research onto a prototypical patient journey in the hospital, along which medical documents are created, processed and consumed by hospital staff and patients themselves. Specifically, we reviewed which dataset types, dataset languages, model architectures and tasks are researched in current clinical NLP research. Additionally, we extract and analyze major obstacles during development and implementation. We discuss options to address them and argue for a focus on bias mitigation and model explainability. While a patient's hospital journey produces a significant amount of structured and unstructured documents, certain steps and documents receive more research attention than others. Diagnosis, Admission and Discharge are clinical patient steps that are researched often across the surveyed paper. In contrast, our findings reveal significant under-researched areas such as Treatment, Billing, After Care, and Smart Home. Leveraging NLP in these stages can greatly enhance clinical decision-making and patient outcomes. Additionally, clinical NLP models are mostly based on radiology reports, discharge letters and admission notes, even though we have shown that many other documents are produced throughout the patient journey. There is a significant opportunity in analyzing a wider range of medical documents produced throughout the patient journey to improve the applicability and impact of NLP in healthcare. Our findings suggest that there is a significant opportunity to leverage NLP approaches to advance clinical decision-making systems, as there remains a considerable understudied potential for the analysis of patient journey data.