Models of noncommutative geometry that are beyond the usual almost-commutative framework that assumes product geometries, may lead to interesting physical theories both in particle physics as well as for cosmological models. In particle physics such theories can describe the Standard Model with no fermion doubling, explicit violation of the CP-symmetry and lead to the appearance  of topological terms in the electroweak sector. Similar approach applied to cosmological models shows features resembling bimetric gravity theories. Based on joint work with Andrzej Sitarz and Paweł Zalecki.