  In this thesis, two aspects of string theory are discussed, tensionless
strings and supersymmetric sigma models.
  The equivalent to a massless particle in string theory is a tensionless
string. Even almost 30 years after it was first mentioned, it is still quite
poorly understood. We discuss how tensionless strings give rise to exact
solutions to supergravity and solve closed tensionless string theory in the ten
dimensional maximally supersymmetric plane wave background, a contraction of
AdS(5)xS(5) where tensionless strings are of great interest due to their
proposed relation to higher spin gauge theory via the AdS/CFT correspondence.
  For a sigma model, the amount of supersymmetry on its worldsheet restricts
the geometry of the target space. For N=(2,2) supersymmetry, for example, the
target space has to be bi-hermitian. Recently, with generalized complex
geometry, a new mathematical framework was developed that is especially suited
to discuss the target space geometry of sigma models in a Hamiltonian
formulation. Bi-hermitian geometry is so-called generalized Kaehler geometry
but the relation is involved. We discuss various amounts of supersymmetry in
phase space and show that this relation can be established by considering the
equivalence between the Hamilton and Lagrange formulation of the sigma model.
In the study of generalized supersymmetric sigma models, we find objects that
favor a geometrical interpretation beyond generalized complex geometry.
