  Out-of-plane polar domain structures have recently been discovered in
strained and twisted bilayers of inversion symmetry broken systems such as
hexagonal boron nitride. Here we show that this symmetry breaking also gives
rise to an in-plane component of polarization, and the form of the total
polarization is determined purely from symmetry considerations. The in-plane
component of the polarization makes the polar domains in strained and twisted
bilayers topologically non-trivial, forming a network of merons and antimerons
(half-skyrmions and half-antiskyrmions). For twisted systems, the merons are of
Bloch type whereas for strained systems they are of N\'eel type. We propose
that the polar domains in strained or twisted bilayers may serve as a platform
for exploring topological physics in layered materials and discuss how control
over topological phases and phase transitions may be achieved in such systems.
