Custom APIs offer a new code-first way to define messages that you can add to Dataverse web services. Conceptually, Custom APIs are an extension to Custom Actions that have provided a no-code way to include custom messages.
Please note that Custom APIs is still a feature in preview.
While Custom Actions allowed you to define your API using the synchronous workflow engine, Custom APIs uses a plugin instead. Custom APIs also add a lot of extra configuration options compared to Custom Actions, including the ability to require a specific privilege to call the API, restrict how custom plugins can be attached to it or hide it from metadata discovery entirely.
Custom API Manager for XrmToolBox by David Rivard
XrmToolBox Integration Tester by Jonas Rapp
CDS Custom APIs by Mark Carrington
Dataverse Custom API: AllowCustomProcessing Explained by David Rivard
Dataverse Custom API: Keep It Private by David Rivard
Dataverse Custom API Manager by David Rivard
Custom API Tester by Jonas Rapp
Collection of Generic Custom APIs by David Rivard