
Once you hit 61 only Marquise and Imperial variants can drop and the older gems you got by leveling can be safely discarded. Non-legendary gems can drop in one of several variants, depending on your level, while you are leveling.A complete list of gems can be found in the official game guide:.Gems can be either a normal gem which can be one of 5 colors (or types) or a legendary gem.I guess if you are a new player you could use a few more points about gems themselves: If you luck is like mine, you will get none of those in season start when they are most needed and then 10 in a row later in a season and have nothing to do with them except let them pile up :-( A special item mentioned in previous replies, Ramaladni's Gift ( ) is a special consumable (one-use) item that will let you add a socket to a weapon (and weapon only) if that weapon does not have a socket.The rest of your sockets are of lower priority. Your most important gem slots are the Jewelry slots (rings and amulet) where you will place legendary gems, weapon (you almost always want a 130% CHD gem in it) and helmet - where typically you will want to use a +%health or +CDR gem, but sometimes +gold if doing a gold farming run or +xp gem if boosting a low level character.

You will find her in Act 5 in story mode. If an item can roll a socket but did not, you can reroll for a socket (among other item mods) using Myriam Jahzia, the Mystic artisan (once you level her up).Chests can roll up to 3 sockets, legs up to 2, everything else only 1 socket. Braces, belt, gloves and boots cannot roll sockets.

You will find Shen in Act 2 in story mode.

To add a few details to the previous (good, but short) answers, gem sockets simply allow you to place a gem in them, using drag-n-drop.
