I lack legal experties, but I'd assume you will easily be able to sue any company and claim they infringe somehow on your rights as stated by this GDPR; maybe I'm wrong.
I attended a GCP event and I could practically see the hipsters pupils dilate/mouth foaming as they went in the hisper frenzy "this GDPR is a huuuge opportunity".
You can write a complaint to responsible institutions that then chose how to act (send a warning to violating company, issue them fine, start an investigation etc.) You cannot sue companies yourself, unless you can prove that (big) damage was done to you as a direct consequence of violation, then you can seek compensation via civil lawsuit.
Max Schrems (who's case killed Safe Harbour) has set up an org None of your Business (https://noyb.eu) to do exactly this.