  The concept of fragility provides a possibility to rank different supercooled
liquids on the basis of the temperature dependence of dynamic and/or
thermodynamic quantities. We recall here the definitions of kinetic and
thermodynamic fragility proposed in the last years and discuss their
interrelations. At the same time we analyze some recently introduced models for
the statistical properties of the potential energy landscape. Building on the
Adam-Gibbs relation, which connects structural relaxation times to
configurational entropy, we analyze the relation between statistical properties
of the landscape and fragility. We call attention to the fact that the
knowledge of number, energy depth and shape of the basins of the potential
energy landscape may not be sufficient for predicting fragility. Finally, we
discuss two different possibilities for generating strong behavior.
