This thesis simultaneously deals with elastic and viscous rods. Their dynamics is ruled by the same set of equations (Kirchhoff equations) despite a difference in their constitutive laws. Using a Lagrangian framework for describing viscous rods lead us to the Discrete Viscous Rods simulator. It was validated against the classic results for the viscous coiling of a filament falling down towards a surface similar to what happens when pouring honey onto a toast. We then studied the fluid mechanical sewing machine. A thin viscous thread falls onto a moving conveyer belt and lays down in a wealth of complex "stitch" patterns depending on the belt speed and the fall height. A numerical phase diagram for the patterns was produced and reproduced the major features of the one found in literature. Fourier analysis of the motion of the thread's contact point with the belt suggests a new classification of the observed patterns, and reveals that the system behaves as a nonlinear oscillator coupling the pendulum modes of the thread. Next we investigate the curling of an initially flat but naturally curved Elastica on surface. Combining experiments, simulations and theory, we find novel behaviour, including a constant front velocity and a self-similar shape of the curl at long times after the release of one end of the Elastica that converge towards a roll of nearly constant curvature located near the free end. Finally we investigate the dynamics of the lasso and explain the flat loop trick with a minimalist model that includes all the major features of what really a lasso is.
