  The topics covered in this thesis may be divided into three parts. Firstly,
we perform a study on the most general branes which are consistent with the
Poisson sigma model, both at the classical and quantum levels. The second part
is devoted to the particular case in which the target Poisson manifold is a
Poisson-Lie group. Finally, we investigate the supersymmetric version of the
twisted Poisson sigma model and its connection with twisted generalized complex
geometry.
