Oculus Rift Touch Controllers

A button = Confirm/Move
X button = Confirm/Move
Trigger Button = Gadget Interaction
Grip Button = Interact Object, Grab/Hold Object (When held), Throw Object (Hold and Release)
Joystick - Turn 180 degrees (While Sitting)
Left Oculus button = Pause
Right Oculus button = Open Steam Overlay/Oculus Universal Menu

HTC Vive Controller

Top of Circle Pad (Press) = Confirm/Move
Bottom of Circle Pad (Press) - Turn 180 degrees (While Sitting)
Top system button = Pause
Bottom system button = Open Steam Overlay
Trigger Button = Gadget Interaction
Side Grip Button = Interact Object, Grab/Hold Object (When held), Throw Object (Hold and Release)

Steam Controller*

(*Note: Arkham VR cannot be played using the Steam Controller with the Oculus Rift):
Joystick = Move Item Around Current Position
Y button = Move
X button = Equip Forensics Scanner/Use Forensics Scanner (When Equipped)
A button =  Interact/Unequip Gadget
B button = Equip/Use Grapnel Gun 
Right System Button = Pause
D-pad Down = Turn 180 Degrees (While Sitting)
Right Bumper button = Equip Batarang, Throw Batarang (when Equipped)

Xbox One Controller

Xbox button = Open Steam Overlay/Oculus Universal Menu
Left Joystick = Move Item Around Current Position
Right Joystick = Rotate Item
Y button = Move
X button = Equip Forensics Scanner/Use Forensics Scanner (When Equipped)
A button =  Interact/Unequip Gadget
B button = Equip Grapnel Gun/Use Grapnel Gun (When Equipped)
Right System Button = Pause
D-pad Down = Turn 180 Degrees (While Sitting)
Right Bumper button = Equip Batarang, Throw Batarang (when Equipped)