Mods

Mod background
Mod or modification is a term generally applied to personal computer games (PC games), especially first-person shooters, role-playing games and real-time strategy games. Mods are made by the general public or a developer, and can be entirely new games in themselves, but mods are not standalone software and require the user to have the original release in order to run. They can include new items, weapons, characters, enemies, models, textures, levels, story lines, music, and game modes. They also usually take place in unique locations. They can be single-player or multiplayer.

Mod safety
Before installing any mods, please note, that mods are not officially a part of Terraria. You must never try to install a mod into the game or server unless it has been updated to exactly match the version of the client you are running. Even a slight variation could be enough to cause problems, including crashing or corrupting your saves/worlds. Mods are typically updated on an irregular schedule shortly after the game itself is updated (though this depends on how quickly the mod author or maintainer gets to it), so there will always be a period following a new release when no mods are safe to use yet.

Mods that only alter the behavior of existing items, blocks, or mobs are fairly safe; they should typically be able to be installed or uninstalled at will, without corrupting your save (although if you have structures that rely on behavior introduced by a mod, then they won't work without the mod installed). Note that this includes mods that add crafting recipes without adding new items/blocks.

Mods that introduce new items, blocks, or mobs are not safe to uninstall. Once you have saved a new item/block/mob into your world, you must never play that world without having the mod installed, or you risk crashes or corruption. (Should you wish to uninstall the mod, you must either abandon your previous saves that used it, or ensure that you destroy all of the new items/blocks/mobs in your world before removing the mod.

Multiple mods may conflict with each other; certainly if two mods need to alter the same files, then they are unlikely to be compatible.

Mod list
Currently, Terraria has mods, but they're rarely allowed on the official forum.

Mods exist that don't require modification of the Terraria executable. For example, tMod. tMod is free and opensource. It's a server modification that protects your server from griefing and gives you administration tools. It also gives you the ability to create plugins in either C#, VB, or even Lua. Soon tMod will even have a client mod that turns Terraria into a sort of... 2D Garry's Mod, using Lua!

tMod webpage