Challenges are optional battles that randomly appear around the World Map. They are represented by small round arenas, and come in three different colors (orange, red and purple) which indicate three different difficulties: Normal, Hard and Epic. Initially, you will only see Normal Challenges around the World Map, but if you complete three Normal Challenges, one Hard Challenge will appear; if you complete four Hard Challenges, one Epic challenge will appear.
Normal Challenges: These are the Challenges that you will usually see around the World Map. They are orange in color, and their power level will be adapted to the average power of your current gladiators. Normal Challenges can be completed at any time, and they will not disappear unless you complete them, but any Normal Challenge that you win will disappear and give you a small "point" in the counter on the bottom left. Also, they reappear several times a day, so you never be out of Normal Challenges for a long time. Their rewards include a Wood Token.
Hard Challenges: One Hard Challenge will appear every time you win your third Normal Challenge. Their power level will be slightly superior to the average power of your gladiators, and they have a time counter of 10 hours; if you don't complete them within that time, they will disappear and you will lose the chance to win them. Every time you win a Hard Challenge, a "point" will be added to the counter in the bottom right. Their rewards are slightly better than Normal Challenges, and include a Silver Token.
Epic Challenges: Whenever you manage to win your fourth Hard Challenge, an Epic Challenge will appear. Their power level will be noticeably higher, and their timer is shorter; only 2 hours. If you can't complete them in those two hours, they will disappear. Their rewards are much better, and include a Golden Token.
Remember that Tokens are redeemable at the Merchant, and that you can obtain fabulous chests filled to the brim with rewards for them.