So, noticed lately that there's been a there's been a lot of questions regarding Trophies and figured I post this up here to try and help people out. If you notice any mistakes or would like to add anything by all means feel free to comment.

Alright lets get started. First thing to know is that in many cases trophies are "Bound". This means they cannot be traded to other players (currently on PC fishing trophies and unused monster trophies can be sent to alts via the bank. Though this may change with future updates *As of Patch 2.1.4 this is no longer possible).

Now, what are trophies and what do they do? Well, there are several different types of trophies:

Quest Trophies
Most of these you'll get for completing quests related to Public Dungeons but a few can be found elsewhere in the world. These trophies are Bound and cannot be traded or sold to other players. They can be banked though.*Note: Patch 2.3.5 has added a new category to Collections called Mementos, so now all these type of trophies will be stored there instead of in the Miscellaneous section of you inventory.

Collecting these kinds of trophies does not count towards any achievement in and of themselves. They provide largely cosmetic effects and are just there for your own personal enjoyment.

Fishing Trophies.
Rare fish are found by (yep, you guessed it) fishing. More specifically from "fishing holes" which can be found in most any body of water. What fish you'll catch depends on zone and the type of water your fishing in. How successful you'll be at actually catching any fish depends on whether or not your using the correct bait and, naturally, a healthy dose of RNG. These trophies are Bound and cannot be traded or sold to other players. Nor can they be banked.

Rare fish that you've caught are automatically registered towards their respective achievements once you pick them up. For completing the different fishing achievements players are rewarded with various different dye colors.

Monster Trophies
These trophies are found as loot drops from vanquished foes and only from enemies who are no more than five levels lower then yourself (for veteran rank players this means no lower than level 45). These trophies are Bound and cannot be traded or sold to other players. Nor can they be banked.

For players on the PC in order to get the trophies to register towards their respective achievement you have to actively "use" the item. For players on Console you need only pick the item up and it should register automatically. *As of patch 2.1.4 Monster trophies for PC now function the same as their Console counterpart. There is no longer any need (or ability) to "use" these kinds of trophy items anymore as they will automatically be registered towards their respective achievements once you've picked them up.

Now, since there's no need to "use" the trophy item this means the item just ends up sitting in your inventory taking up space (*Note: As of Patch 2.1.4 they no longer show up under "Consumables" in your inventory. They have been moved to "Miscellaneous".) It's only natural you'd want to get rid of it at your earliest convenience. However before you do so, check to make sure the item has actually been registered towards your achievements. If it has you can dispose of it as you please. If not hold on to it and file a bug report.

For completing the different collection achievements players are rewarded with various dyes.

Psijic Ambrosia Fragments
Fragments are randomly rewarded for completing daily provisioning writs of any rank but your more likely to get a fragment by completing higher rank writs (though even at max provisioning, the chance of getting a fragment is still pretty low). Combining all seven pieces will create the Psijic Ambrosia recipe.

Fragment are not Bound and can be banked, sold or traded freely. As can the Psijic Ambrosia recipe.

Glass Motif Fragments
Fragments are rewarded randomly for completing daily equipment (blacksmithing/tailoring/woodworking) writs. Combining 10 fragments along with 1 Merithic Restorative Resin (available for purchase from Mystic vendors for 10k gold per unit) will create a random motif chapter.

Fragments are not Bound and can be banked, traded or sold freely. As can completed Glass Motif chapters.

Undaunted Keys
Undaunted Keys come in three types: Bronze, Silver and Gold. Undaunted Keys are "Bound". They cannot be traded, sold or placed in the bank.

Bronze keys are rewarded for doing the Non Veteran difficulty dungeon pledge given by Mag Al-ragath and completing the primary objective.

Silver Keys come from doing Non Veteran difficulty dungeon pledge given by Maj Al-ragath and completing both the primary and optional objectives. As well as by completing the Veteran difficulty dungeon pledge given by Glirion the Redbeard without doing the bonus challenge.

Gold Keys are given for finishing the Veteran difficulty dungeon pledge given by Glirion the Redbeard and doing the bonus challenge he gives.

And there you have it your pocket guide to Trophies. Happy Hunting!