The Yakuza series did not previously sell well in the North American region despite having a vocal fan base. Thus, there was always fear that the new releases in the franchise would never be localized.
Fortunately, the recently released Yakuza 0 renewed interests back into the series. Not to mention that Sega has already confirmed that Yakuza Kiwami and Yakuza 6 are also being localized for the west, with the former slated for release later this summer and the latter coming out in early 2018.
The first Yakuza game came out for the PlayStation 2 in North America in 2006. Yakuza 2 was released for PlayStation 2 in 2008, followed by Yakuza 3 for PlayStation 3 in 2010 and Yakuza 4 for PlayStation 3 in 2011. Yakuza 5, which is digital-only exclusive on the PlayStation Store, came out for the PS3 in late 2015.
So, if you are a new fan of the series and/or a collector, you might want to check out the limited reprint of the first four mainline releases.