Gems

Gems are an item dropped when defeating any kind of Pokémon once the player has the Gem Case unlocked. These typed Gems can be invested into the Gems tab to increase type effectivity, and your damage output. They can also be used to purchase and use flutes.

Helpful tips
The Gems you get from defeating a Pokémon depend on the type(s) that Pokémon has. Wild Pokémon on routes give 1 Gem per type, dungeon encounters give 3, most gym/trainer Pokémon give 5, and dungeon bosses give 20. Battle Frontier Pokémon give gems which number increases as the player progresses further (every 80 stages the number goes up by 1).

Note: Gyms yield 5 Gems per Pokémon, but not every pokemon in a gym will be the appropriate type. The most efficient gyms yield the most Gems per gym clear. (e.g. Violet City Gym is less efficient than the Petalburg City Gym because it takes twice as many clears of the Violet City Gym to obtain the same number of Gems).

Gem Optimization
Note: In the table below, Gems are listed in pokemon type order, and the gyms are listed in the normal gym order, and gyms in bold are considered to be the most efficient gyms.

Alternatively, using the /gems command in the Discord server's #bot-commands channel gives you a list of all routes with a given type in every region.

Total Gym Gems for each gym
        

Type effectiveness chart
Type Effectiveness