This chapter aims to give a comprehensive and critical review of current approaches to temporal reasoning in medical applications, and to suggest future research directions. The chapter begins by presenting the relevant time representation and temporal reasoning requirements. Temporal-data abstraction constitutes a central requirement that presently receives much and justifiable attention. The role of this process is especially crucial in the context of time-oriented clinical monitoring and databases. General AI theories of time do not fully address the identified requirements for medical reasoning and key aspects of mismatch with three well-known general theories of time are pointed out. Temporal data abstraction is then further elaborated. An exposition on the different types of temporal data abstraction is followed by a discussion on various approaches to temporal data abstraction, relating that important task to the tasks of knowledge discovery, summarization of on-line medical records, time-oriented monitoring, exploration of time-oriented clinical data, clinical-guideline-based care, and assessment of the quality of medical care. The modeling of time in medical diagnosis and guideline-based therapy is presented next. A central relation in medical diagnosis is the causal relation, while the predominant reasoning paradigm is that of abductive reasoning. The discussion regarding time-oriented medical diagnosis focuses on the temporal semantics of causality and the integration of temporal and abductive reasoning. The discussion on time-oriented guideline-based therapy focuses on the temporal semantics of clinical guidelines and protocols and the kind of automated support required for guideline-based care. As will be seen, both the diagnostic and therapeutic tasks require a mediator to time-oriented clinical data that can respond to temporal queries regarding both raw data and derived concepts. Electronic patient records and databases of such records are obligatory components of any modern hospital information system; clinicians can do without automated decision support for diagnosis and therapy, but they cannot do without a database of patient records. Time is an intrinsic characteristic of patient data, in particular, chronic patients data; thus, research in time-oriented medical databases is an important component of the overall research in temporal reasoning in medicine. The discussion on the summarization approaches of on-line medical records, presented under temporal data abstraction, gives insights into specific temporal models for the particular clinical databases. In addition, more general considerations about temporal medical databases are presented. In particular the relevant research issues under investigation are listed. Finally, two general time ontologies, proposed by the authors, which cover most of the tasks discussed, are overviewed in more detail. These are Shahar's ontology for knowledgebased temporal-data abstraction, and Keravnou's time-object ontology for medical tasks. The chapter concludes by summarizing what has been done and suggesting issues that need further exploration.