(Please note that this is not a complete list)
see also https://en.wikipedia.org/wiki/COVID-19_apps
for a review of the apps used worldwide see MIT Technology Review (as of 7 May 2020 with updates)

Australia: COVIDSafe app

Technology: Bluetooth Low Energy
Provider: Australian Government
Developer: 
Use: voluntary
Documentation/Source code: https://github.com/AU-COVIDSafe

Austria: StoppCorona app

Technology: Bluetooth Low Energy, Google & Apple API
Provider: Austrian Red Cross
Developer: UNIQA private foundation & Accenture Austria
Use: voluntary
Documentation/Source code: https://github.com/austrianredcross

Czech Republic: eRouska app

Technology: Bluetooth Low Energy
Provider: Ministry of Health
Developer: Consortium of volunteers (Covid19CZ)
Documentation/Source code: https://github.com/covid19cz/

France: StopCovid app

Technology: Bluetooth Low Energy
Provider: French Government
Developer: National Institute for Research in Digital Science and Technology (INRIA) & ANSSI, Capgemini, Dassault Systèmes, Inserm, Lunabee Studio, Orange, Santé Publique France and Withings
Use: voluntary
Documentation/Source code: https://gitlab.inria.fr/stopcovid19

Germany: Corona-warn-app

Technology: Bluetooth Low Energy, Google & Apple API
Provider: German Government
Developer: SAP & Deutsche Telekom
Use: voluntary
Documentation/Source code: https://github.com/corona-warn-app

Hungary: Virus radar

Technology: Bluetooth Low Energy
Provider: Ministry of Innovation and Technology
Developer: Nextsense (original name of app: 'StopCorona!')
Use: voluntary
Documentation/Source Code:
'Virus radar'/'StopCorona!' also deployed in North Macedonia

India: Aarogya Setu app

Technology: Bluetooth Low Energy & GPS
Provider: Government of India
Developer: National Informatics Center, Government of India
Use: download mandatory for government and private sector employees
Documentation/Source code: https://github.com/nic-delhi/AarogyaSetu_Android

Iceland: Rakning C19

Technology: GPS
Provider: Government of Iceland
Developer:
Use: voluntary
Documentation/Source code: https://github.com/aranja/rakning-c19-app

Italy: Immuni App

Technology: Bluetooth Low Energy, Google & Apple API
Provider: Government of Italy
Developer: Bending Spoons
Use: voluntary
Documentation/Source code: https://github.com/immuni-app

Latvia: Apturi Covid app

Technology: Bluetooth Low Energy
Provider: Ministry of Health & Centre for Disease Prevention and Control
Developer: Consortium of Latvian private companies
Documentation/Source Code: available for adaptation in other countries or communities on request (info@apturicovid.lv)

New Zealand: NZ Covid Tracer app

Technology: location tracking by QR Code scanning
Provider: Ministry of Health
Developer:
Use: voluntary
Documentation/Source Code: 

Norway: Smittestopp app

Technology: Bluetooth Low Energy & GPS
Provider: Government of Norway
Developer:
Use: voluntary
Documentation/Source code: https://github.com/djkaty/no.simula.smittestopp

UK: NHS Covid-19 app (the trial of this app has ended on 19 June)

Technology: Bluetooth Low Energy
Provider: NHSX
Developer: VMWare Pivotal Labs
Use: voluntary
Documentation/Source code: https://github.com/nhsx/
Future plans: The government now works on developing a solution based on Google & Apple API

Singapore: TraceTogether

Technology: Bluetooth Low Energy
Provider: Government of Singapore
Developer:
Use: voluntary
Documentation/Source code: https://github.com/OpenTrace-community & https://bluetrace.io

Switzerland: SwissCovid App

Technology: Bluetooth Low Energy
Provider: Federal Office of Public Health
Developer: EPFL & ETH Zürich
Use: voluntary
Documentation/Source code: https://github.com/DP-3T/dp3t-app-android-ch