There are a few different ways that you can play back phone calls. One way is to use a call recorder. This is a piece of equipment that you can purchase that will allow you to record both incoming and outgoing calls. You can then connect the recorder to your computer and playback the recordings at your convenience.
Another way to playback phone calls is through your cellphone service provider. Many providers now offer cloud-based storage of call recordings. This means that once a call is recorded, it is stored online and can be accessed from any device with an internet connection. To playback recorded calls, simply login to your account online and locate the recording you wish to listen to.
Finally, there are also some third-party apps available that enable call recording on mobile phones. These apps typically work by first recording the audio of a call on their servers, and then providing users with a link to the recording which can be played back in a web browser or downloaded for offline listening.