Since 1984 INFN and University of Pisa scientists performing experiments at Fermilab have been running a two-month summer training program for Italian students at the lab. In 1984 the program involved only a few physics students from the University of Pisa, but it was later extended to other INFN groups and to engineering students. Since 2004 the program has been supported in part by the US Department of Energy (DOE) in the frame of an exchange agreement with INFN and has been run by the Cultural Association of Italians at Fermilab (CAIF). In 2007 the Sant’Anna School of Advanced Studies (Pisa) established an agreement with Fermilab to share the cost of four engineering students each year. In the almost 40 years of its history, the program has hosted at Fermilab approximately 550 Italian students from more than 20 Italian universities and from some non-Italian universities. In addition, in the years 2010-2019, with the support of the Italian National Institute of Astrophyics (INAF), the Italian Space Agency (ASI), and CAIF, 30 students were hosted in other US laboratories and universities. The Fermilab training programs spanned from data analysis to design and construction of particle detectors and accelerator components, R/D on superconductive elements, theory of accelerators, and analysis of astrophysical data. At the other US laboratories the offered training was on Space Science. In 2015 the University of Pisa endorsed the program as one of its own Summer Schools. The interns are enrolled as Pisa students for the duration of the internship. They are required to write summary reports published in the Fermilab and University of Pisa web pages. Upon positive evaluation by a University board, students are acknowledged 6 ECTS credits. The entire program is expected to expand further under CAIF management. An agreement has been signed between ASI and CAIF, for ASI to support yearly three two-months fellowships in US space science. In the following we inform on student recruiting, training programs, and final evaluation