The Assignments from Battlefield 4s Multiplayer have been spotted on Battlelog and if one were to rank up high enough in the beta then you could also see them.
Ive taken the liberty to added them to the Wiki. Also note that since most of the assignments are basically the same, except they get harder as they go from bronze to gold, and I wasnt going to make a bunch of stubs that will never be added to, I put them in groups.
Like the Assault Basic, Assault Veteran, etc. were all put on one page. Remember that these are the Multiplayer Assignments so Singleplayer Assignments have yet to be revealed.