  We study multidimensional BSDEs of the form $$ Y_t = \xi + \int_t^T
f(s,Y_s,Z_s)ds - \int_t^T Z_s dW_s $$ with bounded terminal conditions $\xi$
and drivers $f$ that grow at most quadratically in $Z_s$. We consider three
different cases. In the first one the BSDE is Markovian, and a solution can be
obtained from a solution to a related FBSDE. In the second case, the BSDE
becomes a one-dimensional quadratic BSDE when projected to a one-dimensional
subspace, and a solution can be derived from a solution of the one-dimensional
equation. In the third case, the growth of the driver $f$ in $Z_s$ is strictly
subquadratic, and the existence and uniqueness of a solution can be shown by
first solving the BSDE on a short time interval and then extending the solution
recursively.
