The uniaxial extensional viscosity is a fundamental material property of a fluid which characterizes the resistance of a material to stretching deformations. For microstructured fluids, this extensional viscosity is a function of both the rate of deformation and the total strain accumulated. Some of the most common manifestations of extensional viscosity effects in complex fluids are the dramatic changes they have on the lifetime of a fluid thread undergoing capillary breakup. In a pinching thread, viscous, inertial and elastic forces can all resist the effects of surface tension and control the 'necking' that develops during the pinch-off process. The dominant balance of forces depends on the relative magnitudes of each physical effect and can be rationalized by dimensional analysis. The high strains and very large molecular deformations that are obtained near breakup can result in a sharp transition from a visco-capillary or inertio-capillary balance to an elasto-capillary balance. As a result of the absence of external forcing the dynamics of the necking process are often self-similar and observations of this 'self-thinning' can be used to extract the transient extensional viscosity of the material. It can also lead to iterated dynamical processes that result in self-similar spatial structures such as a 'beads on a string' morphology. The intimate connection between the degree of strain-hardening that develops during free extensional flow and the dynamical evolution in the profile of a thin fluid thread is important in many industrial processing operations and is also manifested in heuristic concepts such as 'spinnability', 'tackiness' and 'stringiness'. Common examples encountered in every-day life include the spinning of ultra-thin filaments of silk by orb-weaving spiders, the stringiness of cheese, the drying of liquid adhesives, splatter-resistance of paints and the unexpectedly long life-time of strands of saliva.