List of Field Research tasks and rewards

Please, note that there are always only either: specific amount of stardust, or XP, or just one kind of item, or a particular Pokémon encounter for a single task completed, which means only one of following possible rewards is rewarded for single Field Research task completed not all of them!

Current tasks: January and February 2019
Theme for Field Research tasks in January and February 2019 was not told specific in official sources. However, on January, 2019, there was few Field Research tasks added that rewarded Trainers with Pokémon that are essential to catch to progress Let's Go, Meltan Special Research.

Catching Pokémon related tasks
Following tasks are related to Catching Pokémon through the Encounter Screen. To complete any of following tasks, Trainer has to successfully capture Pokémon, which is either approached in the wild, from Raid Bonus Challenge or reward encounter for other, already completed Research task.

Throwing Poké Balls related tasks
Following tasks are related with performance of throwing any of Poké Balls when catching Pokémon.

Gym and Raid Battle related tasks
Following tasks are related with battling a Gyms or Raid Battles.

Other tasks
Following tasks are related with Hatching Pokémon Eggs, evolving or power-upping Pokémon, earning Candy with Buddy and other basic game actions.

Event-only tasks
Following Field Research tasks were available during the certain events.

Community Day tasks
Following is the list of research tasks exclusively available only for the time of specific Community Days.

Hoenn Celebration tasks
Following is the list of research tasks exclusively available only for the time of Hoenn Celebration.

Feebas Research tasks
On January, 2019, there were Limited Research tasks featuring Feebas available in 3-hour mini-event similarly to Community Day tasks.

Trivia

 * If a Trainer encounters a shiny Pokémon as a research reward, said Pokémon will remain shiny until the Trainer captures it. The Trainer is free to run away and re-encounter the Pokémon and it will always be shiny.