In the Anime
Years ago, Forest's father, Flint, left home to become a great Pokémon trainer and never returned. His mother, Lola, soon followed.
This left his eldest brother, Brock, in charge of the family. Brock took care of them for many years, running the Pewter City Gym at the same time. Although in truth, Brock wanted to travel and become a Pokémon Breeder.
Eventually, Flint returned, allowing Brock to leave on a journey with a trainer he had recently met, Ash.
Flint ran the Gym in Brock's absence, but was ousted from the position when Lola returned home. Lola usurped the title of Gym Leader from Flint and turned the Gym into a Water-type Pokémon Gym, something that angered Forest, who was dedicated to Rock-types.
Brock returned home and was shocked to find what happened. Forest and Brock commiserated with each other over the sad state the Gym had fallen into.
Brock defeated Lola in a Pokémon battle, and convinced her to restore the Gym to its former state. In the process, he gave Forest most of his Pokémon and passed the title of Gym Leader onto him.
This listing is of Forest's Pokémon in the Pokémon anime.