We examine the co-evolution of galaxies and supermassive black holes in the Simba cosmological hydrodynamic simulation. Simba grows black holes via gravitational torque-limited accretion from cold gas and Bondi accretion from hot gas, while feedback from black holes is modeled in radiative and jet modes depending on the Eddington ratio ( f Edd ). Simba shows generally good agreement with local studies of black hole properties, such as the black hole mass-stellar velocity dispersion (M BH − σ) relation, the black hole accretion rate vs. star formation rate (BHAR-SFR), and the black hole mass function. M BH − σ evolves such that galaxies at a given M BH have higher σ at higher redshift, consistent with no evolution in M BH − M . For M BH < ∼ 10 8 M , f Edd is anti-correlated with M BH since the BHAR is approximately independent of M BH , while at higher masses f Edd − M BH flattens and has a larger scatter. BHAR vs. SFR is invariant with redshift, but f Edd drops steadily with time at a given M BH , such that all but the most massive black holes are accreting in a radiatively efficient mode at z > ∼ 2. The black hole mass function amplitude decreases with redshift and is locally dominated by quiescent galaxies for M BH > 10 8 M , but for z > ∼ 1 star forming galaxies dominate at all M BH . The z = 0 f Edd distribution is roughly lognormal with a peak at f Edd < ∼ 0.01 as observed, shifting to higher f Edd at higher redshifts. Finally, we study the dependence of black hole properties with H i content and find that the correlation between gas content and star formation rate is modulated by black hole properties, such that higher SFR galaxies at a given gas content have smaller black holes with higher f Edd .