  We report the recent progress in relativistic mean-field (RMF) and beyond
approaches for the low-energy structure of deformed hypernuclei. We show that
the $\Lambda$ hyperon with orbital angular momentum $\ell=0$ (or $\ell>1$)
generally reduces (enhances) nuclear quadrupole collectivity. The beyond
mean-field studies of hypernuclear low-lying states demonstrate that there is
generally a large configuration mixing between the two components $[^{A-1}Z
(I^+) \otimes \Lambda p_{1/2}]^J$ and $[^{A-1}Z (I\pm2 ^+) \otimes \Lambda
p_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight
increases as the collective correlation of nuclear core becomes stronger.
Finally, we show how the energies of hypernuclear low-lying states are
sensitive to parameters in the effective $N \Lambda $ interaction, the
uncertainty of which has a large impact on the predicted maximal mass of
neutron stars.
