PDF/X is an ISO standard for the exchange of printing data between agency / prepress shop and printer. An important concept of PDF/X is the output intent. This is in most cases an ICC profile which describes the intended output (printing standard). In complete color management chain, the PDF/X output intent is the same icc profile which was used for sepration in photoshop, as CMYK colorspace in the Layout application and as reference for the contract proof.
The most secure version of PDF/X is PDF/X-1a
The whole content of the PDF/X file must be in CMY, Gray or Spotcolor according the final print standard. For processing the PDF/X-1a file in the printing house, there is no need for colormanagement, if the output intent is correct for the final printing process.
If the output Intent is quite different compared to the final printing process (e.g. SWOP but print on newspaper) it is possible to use a PDF colorserver to convert the whole PDF/X-1a with an optimized and controlled devicelink-profile from SWOP to newspaper.
Avoid PDF/X-3
A lot of people think, that PDF/X-3 is the PDF/X variant which should be used, if the PDF/X-file should be color converted on the printers side. This is wrong! A PDF/X-3 file is only valid for the output intent which the creator of the PDF/X-3 file has set.
Compared to PDF/X-1a PDF/X-3 has no advantages during the print productions but adds a lot of possible traps.
Avoid PDF/X-4
PDF/X-4 is based on PDF/X-3 but adds transparencies on top. From the perspective of the printer, this is not a save file format for the exchange of printing data. If PDF/X creator and printer would agree on PDF/X-4 with an additional preflight only allowing the colorspaces of PDF/X-1a, this would allow secure file exchange.
PDF/X-3 and PDF/X-4 as internal format for colorserver workflows
In a strongly controlled environment of an high end pre-press shop it may make sense to use PDF/X-3 or PDF/X-4 as an internal master-formtat for PDF colorservers. The data delivered to the printer should still remain PDF/X-1a.