Thieving Challenges is one of the minor elements of the game, although I recommend against ignoring them altogether, because completing them awards you with additional gold (unfortunately, these usually are small sums), and is connected with unlocking two achievements. Challenges are available in two main missions (the successive chapters of the campaign mode) and in the more complex jobs that you receive from Vittori and Ector. These, however, do not appear in the jobs that you receive from Basso, nor during free exploration of the city.
You can learn which thieving challenges are connected with the mission that you are currently doing, by pausing the game and selecting the statistics window from the pause menu. Apart from that, the information on the thieving challenges is also displayed in the summary window, each time you complete a mission.
There are four thieving challenges, connected with each mission, and they are very different from one another. The first three concern various playing style, e.g. Ghost, where you completely avoid your opponents, or Predator, where you eliminate everyone in your path. The final, fourth, challenge on each list is always the same and it concerns collecting all the Loot and Collectibles.
Unfortunately, thieving challenges often exclude each other, because they can mean completing the entire chapter without attacking the other characters and knocking out a certain number of opponents, both at the same time. If you want to unlock all of the challenges, you need, as a matter of fact, complete them two, or even three, times and this is, in my opinion, a disadvantageous solution because, the reward that you receive for completing them is rather symbolic. You can make the exception in situation when you want to meet the requirements of achievements although, it is not completely necessary even then (there are much more thieving challenges than what is necessary to obtain both achievements).