  A panoply of unconventional electronic states has been observed in moir\'e
superlattices. Engineering similar bosonic phases remains, however, largely
unexplored. We report the observation of a bosonic correlated insulator in
WSe2/WS2 moir\'e superlattices composed of excitons, i.e., tightly bound
electron-hole pairs. We develop a pump probe spectroscopy method that we use to
observe an exciton incompressible state at exciton filling {\nu}_ex = 1 and
charge neutrality, indicating a correlated insulator of excitons. With varying
charge density, the bosonic correlated insulator continuously transitions into
an electron correlated insulator at charge filling {\nu}_e = 1, suggesting a
mixed correlated insulating state between the two limits. Our studies establish
semiconducting moir\'e superlattices as an intriguing platform for engineering
bosonic phases.
