The new SHIELD controller works with the SHIELD TV using a Bluetooth connection. This includes SHIELD TV, SHIELD TV Pro, and SHIELD TV (2015).
Other products supported:
1) SHIELD tablet - full support is coming very soon via a tablet software update.
2) Windows PCs - Wireless support for GeForce-equipped Windows PCs is coming later this year. Today, SHIELD controller works as a WIRED (via USB) Xinput controller for Windows-based PCs running GeForce Experience software. However, in order to run in this configuration, SHIELD controllers requires firmware version 1.0 or later. In order to update SHIELD controller to v1.0, a SHIELD TV device is required.
3) Other Android devices - SHIELD controller works as a basic Bluetooth controller for Android phones and tablets. Advanced features such as haptics, microphone, headset jack, volume control, and IR are not supported.