Can't really recommend any originals in those categories, but Criminal Minds is on Netflix and is probably my favorite Crime/Cop show.
For the historical ones, you have Medici, Borgia (both Renaissance Italy), The Last Kingdom (9th century Saxons), Marco Polo (mostly in Asia), The Tudors (15th century England), Versailles (17th century France), Reign (15th century... Scotland I think?), and probably lots of others. If you wanna go really far back, it has The History Channel's "The Bible" mini-series, which had really good reviews iirc. Haven't watched enough of these series to know which ones to recommend, so just choose by setting, I guess.
As for detective/thrillers, I think most of Marvel's Netflix Originals feature that, especially Jessica Jones and Daredevil. Haven't watched those either though.
i see, well i am surprised to see movie level budget in the such series ---