Is there any app for mobile phones that works with recent version of CiviCRM? We use CiviCRM ver. 4.7.16. and there is one app CiviSync Mobile on Google Play shop, but it doesn't work.
To use your CiviCRM on small screens a responsive theme is all that's needed.
This is an extension that will make the admin menu responsive: https://civicrm.org/extensions/slicknav-web-responsive-admin-menu
I'd recommend not trying to go down the route of making all CiviCRM responsive on all devices. How often do you import spreadsheets on your smartwatch?
Instead, I recommend responsive views/themes for specific areas of the CRM.
A google summer of code did make one app that interfaces with other phone features. I'm not sure why it's not on the google play, but https://github.com/Jagatheesan/CiviDroid---Alpha https://github.com/MounaAnnavarapu/Cividroid-2.0-Dashlets