There has been a rumour that Windows Phone 8 apps will resume where one left off when launched from the start screen, but numerous hands-ons showed the old behaviour of apps restarting when launched from the start screen was in place after all.
Now however it appears that the much desired behaviour is available after all, all with a mere one-line change in the app manifest file.
The Microsoft page notes:
This topic describes how to enable fast app resume for Windows Phone 8 apps. On Windows Phone 8, when the user navigates away from an application, the application is suspended and its state is preserved in memory. If the user returns to the application by pressing the Back button or by using the Task Switcher, the app instance resumes. Because the app was preserved in memory, the app quickly resumes in the same state it was when the user navigated away. This process is called Fast App Switching (FAS). If the app is suspended and the user relaunches the app, such as by tapping on the app name in the app list or tapping the appâ€™s primary Start Tile, by default the old instance of the app is terminated and a brand new instance of the app is created. This process is slower than resuming a suspended app and provides a different user experience. Windows Phone 8 introduces the ability for apps to request that user actions that would typically relaunch the app, such as tapping the appâ€™s Start Tile, instead resume the suspended instance of the suspended app instance, if one exists. This feature is called Fast Resume. For more information on the lifecycle of a Windows Phone app see App activation and deactivation for Windows Phone.
Enabling Fast Resume is easy. It only requires a small change in the app manifest file. However, once you have enabled fast resume, there are a few different options for how your app can manage the back stack of previously visited pages when your app resumes. This topic will walk you through the different ways you can optimize the resume experience.
In addition Direct3D apps will always start where one left off, making life a little bit easier for developers porting apps to Windows 8.
See the page at MSDN here.
Thanks NGReader for the tip.