Say you would like to be able to handle incoming calls, example: each time your phone is ringing, call a specific URL with the incoming phone number as parameter and display this web page directly on my computer screen.
There are a couple of ways you could approach this:
CTI (TAPI/JTAPI) - TAPI (Windows only C library) and JTAPI (Java library) provide PC applications with the ability to monitor/control phone, and receive events/caller ID. The PC application could then launch a browser to a particular URL. Note the CTI interfaces can monitor multiple phones, and are commonly used in a client-server architecture, where an application server uses TAPI or JTAPI to monitor all user devices, and provides events via some RPC mechanism to a client based app of some kind.