1. Literally, to try to see a point past someone or something. If you look past the monument, you can see the country's legislative building in the distance. The teacher looked past the student asking the question to the empty desk at the back of the classroom.
2. To anticipate, plan for, or look forward to a time in the future after some event or situation. We're already looking past this loss to the election in 2075. You need to look past this one decision and see the bigger picture of our company's future.
3. To ignore, disregard, or forgive something; to overlook something. We're willing to look past the incident this time, seeing as it was your first offense, but any future transgressions will result in an immediate termination from the company. What she said was insulting, but she apologized, so I'm going to look past it.
4. To accept, feel better about, move on from, or come to terms with something. Try to look past the short-term problems and realize the potential this project has for long-term benefits. If you can look past its goofy-looking exterior, this car is actually very well made and exceptionally fast.