A model for the dynamics of slender filaments of Herschel-Bulkley fluid is used to explore viscoplastic dripping under gravity and thinning under controlled extension (liquid bridges). The conditions required for fluid to yield are delineated, and the subsequent thinning and progression to pinch-off are tracked numerically. Calculations varying the dimensionless parameters of the problem are presented to illustrate the effect of surface tension, rheology, inertia (for dripping) and gravity. The theoretical solutions are compared with laboratory experiments using aqueous solutions of Carbopol and Kaolin suspensions. For drips and bridges, experiments with Carbopol are well matched by the theory, using a surface tension equal to that of water, even in situations when the fluid is not slender. Experiments with Kaolin do not compare well with theory for physically plausible values of the surface tension. Implications for rheometry and surface-tension inference are discussed. (C) 2010 Elsevier B.V. All rights reserved.