We present a theoretical study of single-particle and many-body properties of twisted bilayer WSe2. For single-particle physics, we calculate the band topological phase diagram and electron local density of states (LDOS), which are found to be correlated. By comparing our theoretical LDOS with those measured by scanning tunneling microscopy, we comment on the possible topological nature of the first moire valence band. For many-body physics, we construct a generalized Hubbard model on a triangular lattice based on the calculated single-particle moire bands. We show that a layer potential difference, arising, for example, from an applied electric field, can drastically change the noninteracting moire bands, tune the spin-orbit coupling in the Hubbard model, control the charge excitation gap of the Mott insulator at half-filling, and generate an effective Dzyaloshinskii-Moriya interaction in the effective Heisenberg model for the Mott insulator. Our theoretical results agree with transport experiments on the same system in several key aspects, and establish twisted bilayer WSe2 as a highly tunable system for studying and simulating strongly correlated phenomena in the Hubbard model.