  This survey paper discusses some of the recent progress in the study of
rational curves on algebraic varieties. It was written for the survey volume of
the priority programme "Global Methods in Complex Geometry", supported by the
DFG.
  To start, we discuss existence results for rational curves on foliated
manifolds. We construct the tangent morphism, define the variety of minimal
rational tangents (VMRT) and name a number of results that show that many of
the geometry properies of a uniruled variety are encoded in the projective
geometry of the VMRT.
  The results are then applied in two different settings. For one, we discuss
the geometry of chains of rational curves on uniruled varieties, show how the
length of a variety can be determined from the VMRT and discuss the concrete
example of the moduli space of vector bundles on a curve.
  On the other hand, the existence results for rational curves can be also be
used to study manifolds which are known NOT to contain rational curves. We
employ this method to study deformations of morphisms. Finally, we look at
families of varieties of canonically polarized manifolds over complex surfaces,
and use non-existence results for rational curves on the base to relate the
variation of the family with the logarithmic Kodaira dimension of the base.
