  We show that moir\'e bands of twisted homobilayers can be topologically
nontrivial, and illustrate the tendency by studying valence band states in $\pm
K$ valleys of twisted bilayer transition metal dichalcogenides, in particular,
bilayer MoTe$_2$. Because of the large spin-orbit splitting at the monolayer
valence band maxima, the low energy valence states of the twisted bilayer
MoTe$_2$ at $+K$ ($-K$) valley can be described using a two-band model with a
layer-pseudospin magnetic field $\boldsymbol{\Delta}(\boldsymbol{r})$ that has
the moir\'e period. We show that $\boldsymbol{\Delta}(\boldsymbol{r})$ has a
topologically non-trivial skyrmion lattice texture in real space, and that the
topmost moir\'e valence bands provide a realization of the Kane-Mele quantum
spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological
insulator. Because the bands narrow at small twist angles, a rich set of broken
symmetry insulating states can occur at integer numbers of electrons per
moir\'e cell.
