A subpoena loses its coercive effect the instant it leaves its own jurisdiction — even within the United States.  When that same subpoena leaves the country, the involvement of a foreign court is necessary to compel testimony or the production of documents. Foreign courts take a very dim view of American-style discovery, so requests for judicial assistance must be carefully crafted, lest they be rejected entirely.  See here for elaboration.

Some resources:  (1) The Hague Conference has published a highly anticipated Guide to Good Practice on the use of video-links in cross-border depositions.  Handy stuff, and available for no cost in PDF form here.  (2) As of summer 2020, Viking Advocates has suspended work in evidence compulsion, but we can happily refer clients to Ted Folkman, who publishes Letters Blogatory and has a wealth of experience in cross-border litigation procedure.  He can be reached via his website at hagueevidence.com.]