Tova Stewart, the little girl who plays Hannah, is deaf in real life, and so are both her parents.
Michael Shannon purposely didn't read up on mental illnesses before taking on the role as Curtis, as this is something the character himself knew little about.
On the DVD commentary, Michael Shannon and the director, Jeff Nichols, both clarify that the daughter was not supposed to have been born deaf but had become deaf a few years before the events of the movie due to an illness like meningitis.
In the DVD commentary, Michael Shannon points out that the pills that Curtis takes are actually mint-flavored Tic Tacs.
The insurance agency in this film that assists in getting the daughter's implant is a real agency with several locations in Ohio, where the movie was filmed.
This is the second film written and directed by Jeff Nichols after Shotgun Stories (2007).
The drilling rig, used by Curtis and Dewart, displays the name of an actual drilling company, "McKay and Gould" of Darlington, PA; just outside East Palestine, OH, approximately 60 miles SE of two of the three filming sites of Lorain and Grafton, OH.