We present accurate and efficient numerical methods to simulate the deformation of drops and bubbles in Stokes flow with surfactant. Both insoluble and soluble surfactant will be considered. For insoluble surfactant, a new boundary integral (BI) method is presented in which a special quadrature originally developed by Helsing and Ojala is used to retain accuracy for close drop-drop interactions (joint work with Sara Palsson and Anna-Karin Tornberg, KTH). For soluble surfactant, we describe longstanding work and recent results on the development of a hybrid or multiscale BI method that resolves a transition layer of bulk soluble surfactant near the interface.