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Flagella and cilia are examples of actively oscillating, whip-like biological filaments that are crucial to processes as diverse as mechanosensing, mucus clearance, embryogenesis and cell motility. quations governing the stability of such an active filament involve linear operators that are not self-adjoint. Critical buckling loads in such non-self-adjoint systems cannot be determined using Euler’s static method but rather by estimating eigenvalues of the associated dynamical problem. I will present recent results that combines noise-less continuum mean field analyses, noisy discrete simulations and analytical first passage time calculations to study the spatiotemporal properties of actively forced filaments moving in a viscous fluid. We find that the system exhibits rich dynamical behavior resulting from the interplay between mechanics (inherent structural elastic instabilities), activity (non-conservative follower forces that pump energy into the system), geometry (that controls the type of bifurcating solutions), and dissipation (due to fluid drag).