We've released a beta version of a significant update to the official Dropbox Swift SDK: SwiftyDropbox 10.0.0-beta.3
This new version has several significant improvements, including support for background sessions, as well as compatibility for Objective-C code bases. You can find more information in the beta release notes and README file.
Please try it out and report any issues or feedback; be sure to include the version number of the SDK you're using when doing so. Thanks!