AsteroidOS watches can be synchronized with a variety of devices given that they install a "synchronization client". This page lists all the known synchronization clients by platform.
An official synchronization application for Android phones named AsteroidOSSync is available to download on F-Droid. This app currently offers the best experience possible with AsteroidOS.
There is currently no application available for iOS phones to synchronize with AsteroidOS watches. As far as we know, there hasn't been any development done on such an app yet.
An official synchronization app for SailfishOS named Starfish has been written using libasteroid. However it is not in a usable state yet due to technical limitations in the current Bluetooth Low Energy stack of SailfishOS. This app requires security features of Bluetooth Low Energy that only work with a kernel patched with a backported Bluetooth subsystem. For this reason, the development of Starfish is now on hold.
Jolla has been contacted about that issue. However, at this point, it is still unclear if and when Jolla will patch the Bluetooth Low Energy stack of their phone operating system. There is then no way to predict if/when Starfish will work for everyone.
A synchronization app for Ubuntu Touch named Telescope has been started by a community member. This app tries to re-use as much code from Starfish as possible so some of their codes is shared in a daemon named asteroidsyncservice which uses libasteroid. However, the development of Telescope has been stopped and the app was left in an unusable. At this point, it is still unclear if and when the app's development will be continued.
A community member created a desktop Linux synchronization app named AsteroidOSLinux. It is written in Python and offers some basic scripting capabilities for AsteroidOS synchronization. The code is written in a way that makes it very easily extendable for your own usages.
A demo of the libasteroid usage named asteroid-ctrl is also available as a C++-written CLI application. This app is cross-platform and doesn't do much on its own but can also be extended for your own usages.
A library named libasteroid encapsulates the Bluetooth Low Energy profiles of AsteroidOS in a simple API. It is written in C++ using QtBluetooth and is then cross-platform. Its code can be used as a reference implementation for other clients development or as a 3rd party library.