  In this contribution we present a general procedure that allows the
construction of noncommutative spaces with quantum group invariance as the
quantization of their associated coisotropic Poisson homogeneous spaces coming
from a coboundary Lie bialgebra structure. The approach is illustrated by
obtaining in an explicit form several noncommutative spaces from (3+1)D (A)dS
and Poincar\'e coisotropic Lie bialgebras. In particular, we review the
construction of the $\kappa$-Minkowski and $\kappa$-(A)dS spacetimes in terms
of the cosmological constant $\Lambda$. Furthermore, we present all
noncommutative Minkowski and (A)dS spacetimes that preserved a quantum Lorentz
subgroup. Finally, it is also shown that the same setting can be used to
construct the three possible 6D $\kappa$-Poincar\'e spaces of time-like. Some
open problems are also addressed.
