  We investigate $S=-1$ and $-2$ hypernuclei with $A=4-8$ employing the
Jacobi-NCSM approach and in combination with baryon-baryon interactions derived
within the frame work of chiral effective field theory. The employed
interactions are transformed using the similarity renormalization group (SRG)
so that the low- and high-momentum states are decoupled, and,
thereby,convergence of the binding energies with respect to model space can be
significantly speeded up. Such an evolution is however only approximately
unitary when the so-called SRG induced higher-body forces are omitted. We first
explore the impact of the SRG evolution on the $\Lambda$ separation energies
$B_{\Lambda}$ in $A=3-5$ hypernuclei when only SRG-evolved two-body and when
both two- and three-body forces are included. For the latter scenario, we
thoroughly study predictions of the two almost phase-equivalent NLO13 and NLO19
YN potentials for $A=4-7$ hypernuclei. The NLO19 interaction yields separation
energies that are comparable with experiment, whereas NLO13 underestimates all
the systems considered. We further explore CSB splittings in the $A=7,8$
multiplets employing the two NLO YN potentials that include also the leading
CSB potential in the $\Lambda$N channel, whose strength has been fitted to the
presently established CSB in $A=4$. Finally, we report on our recent study for
$\Xi$ hypernuclei based on the $\Xi$N interaction at NLO.
