  The global polarization of the $\Lambda$ and $\bar\Lambda$ hyperons ($P_{\rm
H}$) has been measured in Pb--Pb collisions at $\sNN=$ 2.76 TeV and 5.02 TeV in
ALICE at the Large Hadron Collider (LHC). The hyperon global polarization is
found to be consistent with zero at both collision energies. The local
polarization of the $\Lambda$ and $\bar\Lambda$ hyperons along the beam ($z$)
direction, $P_{\rm z}$, has also been measured in Pb--Pb collisions at
$\sNN=5.02$ TeV. The $P_{\rm z}$, measured as a function of the hyperon
emission angle relative to the second harmonic symmetry plane, exhibits a
second harmonic sine modulation, as expected due to elliptic flow. The
measurements of global and local hyperon polarization are reported for
different collision centralities and as a function of transverse momentum in
semicentral collisions. These results show the first experimental evidence of a
non-zero hyperon $P_{\rm z}$ in Pb--Pb collisions at the LHC.
