This talk will provide an overview of our recent work on amplification of disturbances in channel flows of viscoelastic fluids. Even if a standard linear stability (i.e., modal) analysis predicts that a particular flow is stable, the question of the sensitivity of the flow to various disturbances remains. If disturbances to the linearized governing equations are sufficiently amplified over a finite time interval, then nonlinearities may become important and cause transition to a more complex flow state. This can happen if the underlying linear operator is non-normal, and represents a non-modal mechanism of disturbance amplification. We address this issue by adopting an input-output point of view borrowed from the systems- and control-theory communities. The inputs to the linearized equations consist of spatially distributed and temporally varying body forces that are harmonic in the streamwise and spanwise directions and stochastic in the wall-normal direction and in time. Such inputs enable the use of powerful tools from linear systems theory that have recently been applied to analyze Newtonian fluid flows. We find that the most amplified disturbances are three-dimensional in nature, and that large amplification can occur under conditions of weak inertia and strong elasticity. The underlying physical mechanism involves polymer stretching that introduces an effective lift-up of flow fluctuations similar to vortex-tilting in inertia-dominated flows. The mechanism examined here provides a possible route for a bypass transition to elastic turbulence and might be exploited to enhance mixing in microfluidic devices. (Joint work with Mihailo Jovanovic, University of Minnesota.)