Investigations are Green spheres scattered throughout the game. They are bits of information related to the plot of the gameplay surrounding them. Finding all items within a single Investigation will yield a reward that you will receive in the in-game email. Bellow is a list of all the Investigations we have encountered in the game so far with in-game screenshots for each collection item and its location. Investigations we have completed will also have their reward listed (and screenshot provided). You can sort the Investigation table by clicking on the headers for that column and you can visit the detailed screenshot walkthrough page for the Investigation by clicking on its name.

Ace Chemical AnalysisGothamGotham6/6
Against the HIVEMetropolisLittle Bohemia6/6
Amulets of MemoryMetropolisDowntown6/6
Arkham Session NotesGothamGotham6/6
Artifacts of ThemysciraMetropolisChinatown6/6
Azarathian Sin GemsMetropolisMidtown7/7
Barry Allen's Case NotesDuoFlashback4/4
Behind the WallAlertsStryker's Island8/8
Cadmus Research FindingsAlertsArea 515/5
Concentrated Chemical SamplesAlertsBludhaven5/5
Confiscated ArcanumMetropolisChinatown6/6
Corrections Officer\\\'s ReportMetropolisStrykers/shipyards6/6
Creatures of the ShadowlandsMetropolisHistoric District6/6
Crystalline Soul FragmentsMetropolisChinatown6/6
Dr. Arkham's Observation JournalAlertsArkham Asylum8/8
Enigmatic PuzzlesGothamOtisburg6/6
Falcone's FinestGothamBurnley6/6
Ferris ReelsAlertsCoast City5/5
Files of T.O. MorrowAlertsAce Chemical8/8
Five-Clawed TreasuresGothamGotham University Warehouse6/6
From the War FrontGotham Under SiegeGotham Under Siege 
Frozen HeartGothamBurnley6/6
Ghost in the MachineGothamOtisburg6/6
Gorilla Bomb ComponentsMetropolisLittle Bohemia6/6
Gorillatech SchematicsMetropolisDowntown6/6
Gotham Gone to HellGotham WastelandsGotham Wastelands6/6
Hall of Doom Holographic TokensHall of DoomHall of Doom4/4
Hope for the HopelessBattlezoneMetropolis4/4
Infiltrating the Hall of DoomThe Hall of DoomThe Hall of Doom6/6
Infiltrating the WatchtowerWatchtowerWatchtower6/6
Legal EagleGothamBurnley6/6
Lexcorp Cloning RecordsLexcorp Cloning FacilityLexcorp Cloning Facility4/4
LexCorp Genome DatabaseMetropolisLittle Bohemia7/7
Lunar Exobyte ClustersAlertsHIVE Moon Base6/6
Lunar SilverMetropolisMidtown6/6
Morrow's Magnificent MechaniksGothamOtisburg6/6
No Man EscapesMetropolisHistoric District6/6
Oaths of LightMetropolisDowntown8/8
Pernicious PicturesGothamOtisburg6/6
Power Armor Integration CircuitsGothamEast End6/6
Ritual Canopic JarsGothamBurnley6/6
Rose By Any Other NameGothamBurnley6/6
Signs of the BeastMetropolisTomorrow District6/6
Simalien TechnologyGorilla IslandGorilla Island5/5
STAR Materials HandlingMetropolisLittle Bohemia6/6
Steelworks Robot ProtocolsMetropolisSteelworks area6/6
The Atlantis ChronicleMetropolisSuicide Slums6/6
The Battle For ContainmentAlertsWatchtower Containment8/8
The Battle for the ArmoryAlertsHall of Doom Armory8/8
The Doctor Is InMetropolisLittle Bohemia5/5
The Flame of Change CodexRaidGates of Tartarus4/4
The Island of Dr. MorrowAlertsOolong Island5/5
The Precipice of FearGothamEast End6/6
The Tenets of CrimeGothamBurnley5/5
The Voice of DoomAlertsSmallville5/5
Tools of the TradeRaidBatcave3/9
Trigon Tainted ArtifactsMetropolisTomorrow District5/5
Twisting the TitansGothamRobinson Park6/6
Viva la Lucha LibreGothamEast End6/6
Watchtower Holographic TokensWatchtowerWatchtower4/4
World War III RemnantsRaidKhandaq5/5