There is an official dedicated website about this argument. They key of new Privacy law is below indicated:
"After four years of preparation and debate the GDPR was finally approved by the EU Parliament on 14 April 2016. Enforcement date: 25 May 2018 - at which time those organizations in non-compliance may face heavy fines.
The EU General Data Protection Regulation (GDPR) replaces the Data Protection Directive 95/46/EC and was designed to harmonize data privacy laws across Europe, to protect and empower all EU citizens data privacy and to reshape the way organizations across the region approach data privacy. The key articles of the GDPR, as well as information on its business impact, can be found throughout this site."
Key changes are here indicated.
More resources might be found here.
<=======>
Meanwhile, about italian country, I would like to mention this .PDF file that give a quickly overview about changes that are going to be requested/applied.
I am going to share this link and file for whom that would like to have an overview.
Guida all applicazione del Regolamento UE 2016 679.pdf (3273 k)
There is an interesting website feature that permit you to listen to document
To be strictly updated with Garante della Privacy (italian and English languages are available) there are RSS too.
[update 2018.05.01]
I would like to mention this article that explain that, if European citizen data are treated in any other country (external European community), that data need to managed following GDPR regulation, here it is an interesting article that well explain concept
https://www.technologyslegaledge.com/2017/06/global-reach-of-the-gdpr-what-is-at-stake/#page=1
[update 2018.06.17]
I would like to mention this .pdf Microsoft link about ""
Download "Microsoft's Journey to Compliance" .pdf
Microsoft link explanation:
https://resources.office.com/ww-landing-M365E-GDPR-microsoft-journey-to-compliance-ebook.html
[update 2018.07.17]
Correct download link:
Guida all applicazione del Regolamento UE 2016 679.pdf (3273 k)
https://www.garanteprivacy.it/documents/10160/0/Guida+all+applicazione+del+Regolamento+UE+2016+679.pdf