Legends:Twitch Drops

Twitch Drops is a major promotion for Legends, offering in-game rewards for streaming or watching the game on Twitch. The promotion began on June 11, 2017 for Bethesda's E3 Showcase livestream, and was rolled out to all users on June 14, 2017. It was announced as the first step towards further Twitch integration.

To receive drops, you must first go to Bethesda.net and link your Bethesda account with your Twitch account. Once this is done, you can either stream or watch Legends on Twitch to begin getting drops. Drops must be enabled for each livestream, and you can see if a stream has them enabled under the video. The words "Drops enabled! Watch for a chance to earn loot" will appear on the left side, under the video screen on PC. Drops are enabled if the streamer has linked their Twitch account with Bethesda.net and if the stream has more than one viewer. Should you get a drop, you will receive a whisper (private message) from the official "Bethesda" account on Twitch. Your reward will be automatically redeemed the next time you log into Legends.

Twitch Drops were discontinued on September 17, 2018, with the exception of special events such as the official weekly stream and select tournaments and presentations. They were re-enabled for all livestreams on April 11, 2019.

Drops
Originally, one drop could be obtained on average every 24 hours. The three potential rewards you could earn as drops were:
1,500 Soul Gems
1 Core Legendary Pack
600 Gold

On August 4, 2017, four new drops were added to the existing pool of drops. This came along with changes to how frequently drops can be obtained. Specifically, drops now appear to be capped at one every six hours. While still possible, this makes it less likely for a drop to appear only after several days or more. The new rewards you can earn as drops are as follows:
50 Soul Gems
100 Soul Gems
50 Gold
100 Gold

On December 6, 2017, new drops were added to the existing pool of drops:
1 Standard Core Pack
1 Skyrim Pack
3 Arena Tickets

Extensions
 
Extensions are tools that Twitch streamers can apply to their streams. Bethesda created their own for their E3 2018 presentation, which requires viewers to link their ESO and Bethesda.net accounts to receive rewards while watching the stream. 

The awards for Legends in this reward pack are:
2 Houses of Morrowind Packs
2 Heroes of Skyrim Packs
1500 Soul Gems
3 Arena Tickets
An exclusive BE3 Card Back (not distributed until the new game client went live)

To ensure that the extension is enabled, you may click the puzzle-piece icon in the bottom right corner of the stream. Note that extensions are not supported on all platforms yet; it is recommended to view it on PC.

Notes
Although drops are random and several days might pass between drops, unlinking and relinking your Bethesda.net and Twitch accounts might help if you think there's an issue.
As of September 21, 2017, drops no longer work with vodcasts. However, eventually, once Twitch updates their API to add a flag for vodcasts, the Legends drops will be available for vodcasts with a lower probability than drops from normal streams.
Between December 1 and 4, 2017, Return to Clockwork City Act I drops were added to the existing pool. They could be obtained even after pre-ordering the story, which effectively rendered the drops useless for those people.

See Also
Twitch - The Elder Scrolls: Legends — A list of current Legends livestreams.
Bethesda.net - Introducing Twitch Drops
Announcing Our #BE3 Twitch Extension
ESO Twitch Integration
Login Rewards - Another way to earn rewards