DAVdroid is an open-source CalDAV/CardDAV synchronization app for Android 4+.
* two-way-synchronization (server ? client, server always wins)
* focused on simplicity, security and privacy
* supports contacts, calendars (events) and tasks (to-do's)
* lightweight application, not cluttered with "features"
* flawless integration with device and address book/calendar apps
* high-performance algorithms
* separately usable (either CalDAV or CardDAV)
* free and open-source software (FOSS)