In the field of fluid flow within the human body, blood flow in the systemic circulation has been the main focus since the recognition by William Harvey that blood was in fact in continuous circulation and carried by a network of blood vessels. But beyond the systemic circulation, other fluids and other fluid flow phenomena pervade the body so totally that it would be hard to imagine a bodily function of any kind that does not involve fluids or fluid flow. In fact, the study of the systemic circulation is limited to not only the type of fluid involved but also to the type of service which the systemic circulation provides - the first being blood, of course, the second is transport - the principal function of the systemic circulation is to provide a means of transporting blood continuously from the heart to tissue cells and back again. Some of the most fascinating fluid flow phenomena within the human body involve fluids other than blood and a service other than transport- the lymphatic and pulmonary systems provide two striking examples. In this paper we outline the special fluid mechanics of these two systems. While transport is still involved in both cases, this is not the only service which they provide and blood is not the only fluid involved. In both systems, filtration, extraction, enrichment, and in general some “treatment” of the fluid itself is the primary function. In the pulmonary system, the liquid lining of the lungs plays a pivotal role, and the mechanical interaction between tissue and liquid is of key importance to lung viability. In disease states such as respiratory distress syndrome, the lining fluid can become dysfunctional, leading to reduced gas exchange and damage to sensitive pulmonary tissues. The study of the systemic circulation has also been conventionally limited to treating the system as if it were an open-loop system in which the main hemodynamic variables such as pressure and flow are governed by the laws of fluid mechanics independently from the physiological controls and regulations that govern these same variables. This implies that any failure of the system can be fully explained in terms of the laws of fluid mechanics, which of course is not the case. While a system failure due to a physical obstruction in a blood vessel can be readily explained in terms of the laws of fluid mechanics, a system failure due to arrhythmia cannot. In this paper we examine the clinical implications of these issues and of the special biofluid mechanics issues that arise in the lymphatic and pulmonary systems.