In a quest to develop simple and reliable methods for the measurement of viscosity and other non-Newtonian fluid parameters, considerable effort has been expended in examining and establishing the suitability of the flows produced by falling objects (sphere, needle, cylinder), rolling ball and rotating sphere, vibrating sphere, etc. Over the years, it has been demonstrated convincingly that while most of these devices yield reliable values of shear viscosities for Newtonian fluids, their applicability to non-Newtonian fluids is severely limited by the fact that all such flows are nonviscometric. Therefore, neither the shear stress nor the shear rate are uniform, nor are these known a priori. However, most non-Newtonian fluids (except for visco-plastic and time-dependent fluids) approach the Newtonian fluid behavior in the limit of vanishingly small Reynolds and Deborah (or Weissenberg) numbers. It is thus possible to evaluate some characteristics of visco-inelastic and visco-elastic fluids from suitable data obtained from falling object tests under appropriate conditions. This chapter presents an overview of the developments in this field. In particular, consideration is given to the falling ball method, the falling cylinder method, and the rolling ball method. Other less common methods such as rotating and vibrating sphere devices, bubble viscometer, etc. are also mentioned briefly. In order to maintain the consistency of the style of presentation, a short section on the use of each device to measure the viscosity of Newtonian fluids is included which serves as the background for the subsequent discussion for non-Newtonian fluids.