Stochastic integer programming (SIP) problems combine the power of integer decision variables for modeling discrete decisions and logical relationships with the power of stochastic programming for operating, planning, and designing systems under uncertainty. Because of this combination, SIP can be useful in a wide range of applications including power grid operation, employee staffing, and supply chain network design. This combination of features also leads to models that can be extremely difficult so solve. We present an overview of the branch-and-cut solution approach for SIP problems and results of recent research into new methods for generating cuts that can significantly improve the solution times. This work is joint with Rui Chen.