There are various Game Modes available in-game from Solo to Co-op.
Solo
In Solo, you will find various game modes, where you can obtain Materials, Shards, Chips, and complete the main storyline.
Peacekeeping Handbook - this is the main storyline game mode.
Supply - obtain materials for upgrades.
Hero Trial - obtain Shards for completing a challenge.
Night Ops - timed boss battles to obtain Chips.
Co-op
In Co-op, you will be able to take on challenges with your friends.
Agency Assessment - players can team up to take on challenges together.
Joint Operation - team up with other players, and receive rewards.
VS
In VS you will find PvP matches, where you can test your skill against other players.
Arena - 1 v 1 area where you face off against your opponent. Each have 3 Heroes, first to KO all 3 Heroes wins (or whoever has the least amount of Heroes KO'd).
Super Co-op Battle - this is an auto-combat styled PvP, where you set your attack/defense formation and battle other teams.