Cortana expands her reach today beyond the confines of Windows 10 and out to Android and iOS devices. To put it another way: you can now download the Cortana app on your smartphone.
Available functions include location-based reminders (e.g. "pick up wine next time I'm near the grocery store"), text reply to phone calls from your PC, flight and package tracking, and synchronized AI. Functions that aren't available on iOS and Android include toggling settings, opening apps, and invocation of hands-free use (you'll have to use your hands to do that, although it does work for Android users if in the Cortana app or on the Android home screen).
Cortana is available on iOS8+ and Android 4.1.2 starting today in the US and China (see the links below for downloads). Later in December, it will be available for Cyanogen devices in the US. Cyanogen will support special Cortana functions: hands-free invocation, a network mode toggle, power down, and Quiet Mode, among others.