Coulomb interaction plays a fundamental role in condensed matter physics. Despiteits simple form, i.e. 1/r, strong Coulomb correlation is responsible for a plethora of interesting and complex many-body phenomena of electrons, including the fractional quantum Hall effect, Mott insulator, Wigner crystal, superconductivity, etc. In this thesis, we study another example of Coulomb interaction and many body physics: excitons. An exciton forms from Coulomb attraction between a negatively charged electron and a positively charged hole. Exci-ton, as the name suggests, is often observed as an excited state in semiconductors under light. In contrast to this common picture, we demonstrate the creation of an exciton fluid existing in thermal equilibrium in Coulomb-coupled electron-hole bilayer made of two-dimensional semiconductor MoSe2/WSe2 separated by a thin insulating barrier of hBN. The ground state, known as an excitonic insulator, appears when the exciton binding energy exceeds the semiconductor band gap, first proposed by theory in the 1960s. The excitonic insulator hosts bosonic excitations with different quantum statistics compared to the free fermionic constituents. Unlike free electrons or holes, excitons are not subject to Pauli exclusion principle. Below a critical temperature, all excitons can occupy the same ground state, leading to a collective and macroscopic scale behavior, the Bose-Einstein condensate. By physically separating the electron and hole layers, we perform a suite of measurements including thermodynamic compressibility, electronic transport and optical spectroscopy to investigate the many-body physics among excitons (chapter 2 and 3), between excitons and free fermions (chapter 4 and 5). Last, we present an outlook on the possibility of a superfluid state , a dissipationless flow of excitons, as well as further interplay between excitons and topology by putting them on an artificial moire lattice (chapter 6).