Transmission expansion planning (TEP) is a complex decision making process that requires comprehensive analysis to determine the time, location, and number of electric power transmission facilities that are needed in the future power grid. This dissertation investigates the topic of solving TEP problems for large power systems. The dissertation can be divided into two parts. The first part of this dissertation focuses on developing a more accurate network model for TEP study. First, a mixed-integer linear programming (MILP) based TEP model is proposed for solving multi-stage TEP problems. Compared with previous work, the proposed approach reduces the number of variables and constraints needed and improves the computational efficiency significantly. Second, the AC power flow model is applied to TEP models. Relaxations and reformulations are proposed to make the AC model based TEP problem solvable. Third, a convexified AC network model is proposed for TEP studies with reactive power and off-nominal bus voltage magnitudes included in the model. A MILP-based loss model and its relaxations are also investigated. The second part of this dissertation investigates the uncertainty modeling issues in the TEP problem. A two-stage stochastic TEP model is proposed and decomposition algorithms based on the L-shaped method and progressive hedging (PH) are developed to solve the stochastic model. Results indicate that the stochastic TEP model can give a more accurate estimation of the annual operating cost as compared to the deterministic TEP model which focuses only on the peak load.