  We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the
sense that the diffusive properties strongly deviate from the ones of standard
Brownian motion. We first briefly review the concept of transient work FRs for
stochastic dynamics modeled by the ordinary Langevin equation. We then
introduce three generic types of dynamics generating anomalous diffusion:
L\'evy flights, long-time correlated Gaussian stochastic processes and
time-fractional kinetics. By combining Langevin and kinetic approaches we
calculate the work probability distributions in the simple nonequilibrium
situation of a particle subject to a constant force. This allows us to check
the transient FR for anomalous dynamics. We find a new form of FRs, which is
intimately related to the validity of fluctuation-dissipation relations.
Analogous results are obtained for a particle in a harmonic potential dragged
by a constant force. We argue that these findings are important for
understanding fluctuations in experimentally accessible systems. As an example,
we discuss the anomalous dynamics of biological cell migration both in
equilibrium and in nonequilibrium under chemical gradients.
