There are 2 arrow buttons above the item list. Double-clicking again will turn off the search mode. Items that do not match the current search will be grayed out. Double-clicking the search box will visually filter any inventories, including all chests for items that match the search field's criteria. Both of these keys can be changed in the mod's config file. Hovering over an item and pressing the 'R' key (for Recipe) will display that item's recipe while pressing the 'U' key (for Use) shows what that item can be used to create through crafting grids. JEI's search box can be seen from (almost) any GUI in the bottom right of the screen. JEI has a lot of addons, generally adding extra modded recipe support like Thaumic JEI. This list is useful for checking recipes and uses for items, and can also be used to search for items in opened GUIs. This list can be searched via a text box at the bottom. Based off of NEI, JEI modifies the existing Inventory GUI by adding an icon list of items to the far right. JEI, or Just Enough Items, is a utility mod made by mezz.
