The Infinity Stones have changed hands various times over the history of the MCU, some more than others.
(click all images to embiggen)
These are the current and previous owners:
#These are the current and previous owners:
(source film in brackets, index at bottom of answer)
##Space Stone is owned by Asgard/Loki
Space Stone is owned by Asgard/Loki
Excluding all details (Trailers, interviews, theories based on evidence, etc.) from Infinity War, the Space Stone is believed to be destroyed by Surtur along with Asgard.
Including the extra details, this Q&A as Loki having stolen it from the vaults in Asgard before Surtur destroyed Asgard, and as shown in this image from the trailer.
Previous Owners include: Heimdall (AV), Loki (AV), S.H.I.E.L.D. (post-CA:TFA), Howard Stark (CA:TFA), Hydra (CA:TFA), "Church Keeper" (CA:TFA)
##Mind Stone is owned by Vision
Mind Stone is owned by Vision
The Avengers claims the Mind Stone from Ultron when they steal the cradle with Ultron's new body in it. Thor, Stark, and Bruce Banner grant the body life, creating Vision.
Previous owners include: Ultron (AV:AOU), Avengers (AV:AOU), Hydra (AV: AOU), S.H.I.E.L.D (AV), Loki (AV)...
##Reality Stone is owned by Taneleer Tivan (The Collector)
Reality Stone is owned by Taneleer Tivan (The Collector)
The Asgardians gave the Aether (and the Reality Stone) to The Collector for safe-keeping after defeating Malekith.
Previous owners include: Asgard (T:TDW), Malekith (T:TDW), Jane Foster (T:TDW)...
##Power Stone is owned by Nova Corps
Power Stone is owned by Nova Corps
The Power Stone is given to the Nova Corps for safe-keeping after Peter Quill catches the unprotected Stone and destroys Ronan the Accuser.
Previous owners include: Ronan the Accuser (GotG), Star-Lord (GotG)...
##Time Stone is owned by Doctor Strange
Time Stone is owned by Doctor Strange
Doctor Strange owned the gem as part of the Eye of Agamotto, the stone was used by Doctor Strange, first to aid him in his learning of sorcery, then in his final fight against Kaecilius and Dormammu. It is unknown how long the Stone has stood as part of the Eye on a pedestal in Kamar-Taj.
Previous owners include: Cagliostro (DS), Agamotto (DS)
##Soul Stone is Unknown
Soul Stone is Unknown
The location of the Soul Stone is revealed for the first time in Avengers: Infinity War
Key to films:
- CA:TFA = Captain America: The First Avenger
- AV = Avengers
- AV:AOU = Avengers: Age of Ultron
- T:TDW = Thor: The Dark World
- GotG = Guardians of the Galaxy
- DS = Doctor Strange