  We consider inverse boundary value problems for elliptic equations of second
order of determining coefficients by Dirichlet-to-Neumann map on subboundaries,
that is, the mapping from Dirichlet data supported on $\partial\Omega\setminus
\Gamma_-$ to Neumann data on $\partial\Omega\setminus \Gamma_+$. First we prove
uniqueness results in three dimensions under some conditions such as
$\bar{\Gamma_+ \cup \Gamma_-} = \partial\Omega$. Next we survey uniqueness
results in two dimensions for various elliptic systems for arbitrarily given
$\Gamma_- = \Gamma_+$. Our proof is based on complex geometric optics solutions
which are constructed by a Carleman estimate.
