Trajectory optimization and control for spacecraft orbit transfers have received a lot of attention during the past few decades in rendezvous, orbit maintenance, and interplanetary missions. Low-thrust transfers are of particular interest due to the advantages of low-thrust propulsion over chemical propulsion. However, the resulting trajectory optimization problem is challenging to solve because a large number of revolutions may be needed to complete the transfer, and computational challenges may exist due to the long duration of the transfer. In our lab, we are exploiting effective structures of the problem and developing real-time convex optimization algorithms and machine learning approaches for onboard orbit transfer applications.