It's not uncommon to want to get back with your ex after you've split. Sometimes, you want to get back with your ex even if s/he cheated on you and that's what ended the relationship. It's easy for outsiders to look at your situation and judge or give advice – most of which consists of “NO!” The inside of a relationship are different from what everyone sees, however, and the issues therein are personal to every couple. Maybe your ex just made a mistake. Maybe s/he had lots of affairs. Whatever the case, at least consider these points before you decide to give your cheating ex another shot.
What do you love about your ex? What do you dislike about her or him? Weigh up your issues, look at the circumstances of the cheating, and reflect on your happiness as a couple. Is it worth potential heartbreak? If it was one night of cheating or a short, purely sexual affair, can you forgive and move on, or is the trust irrevocably broken?