  In this thesis I discuss analytical approaches to disordered systems using
field theory. Disordered systems are characterized by a random energy landscape
due to heterogeneities, which remains fixed on the time scales of the phenomena
considered. I focus specifically on elastic interfaces in random media, such as
pinned domain walls in ferromagnets containing defects, fluid contact lines on
rough surfaces, etc. The goal is to understand static properties (e.g. the
roughness) of such systems, and their dynamics in response to an external
force. The interface moves in avalanches, triggered at random points in time,
separated by long periods of quiescence. For magnetic domain walls, this
phenomenon is known as Barkhausen noise. I first study the model of a particle
in a Brownian random force landscape, applicable to high-dimensional
interfaces. Its exact solution for a monotonous, but time-varying driving force
is obtained. This allows computing the joint distribution of avalanche sizes
and durations, and their spatial and temporal shape. I then generalize these
results to a short-range correlated disorder. Using the functional
renormalization group, I compute the universal distributions of avalanche
sizes, durations, and their average shape as a function of time. The
corrections with respect to the Brownian model become important in sufficiently
low dimension (e.g. for a crack front in the fracture of a solid). I then
discuss connections to the rough phase of Kardar-Parisi-Zhang nonlinear surface
growth, and an application to the variable-range hopping model of electric
conductance in a disordered insulator.
