Since 1984 the INFN groups have been running a 2-month summer training program for Italian students at Fermilab. In 1984 the program involved only a few physics students from the Pisa group, but it was later extended to other groups and to engineering students. Since 2004 the program has been supported in part by DOE in the frame of an exchange agreement with INFN. In 2007 the Sant’Anna School of Advanced Studies (Pisa) established an agreement with Fermilab to share the cost of 4 engineering students each year. In the 34 years of its history, the program has involved approximately 500 Italian students from more than 20 Italian universities and from some European universities. In the years 2010-2017, with the support of INFN, INAF, ASI, ISSNAF and the Cultural Association of Italians at Fermilab (CAIF), 20 students were hosted in several 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, analysis of astrophysical data. In 2015 the University of Pisa created an ad-hoc Summer School. Fermilab interns are enrolled at the University of Pisa 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 of a University of Pisa committee, students are acknowledged 6 ECTS credits. In 2017 a new agreement with the summer school "MovingKnowledge17" promoted by Oxford University and dedicated to neutrino physics allowed to 3 Fermilab summer students to spend also 4 weeks at Oxford working with the local groups. The entire program will grow under CAIF management. INFN has granted his sponsorship to CAIF, and an agreement has been negotiated between CAIF and ASI for fellowships in US space science laboratories supported by ASI. The program is also part of the outreach of the European Projects MUSE (H2020-MSCA-RISE-2015, GA 690835) and NEWS (H2020-MSCA-RISE-2016, GA 734303). We report on recruiting method, training programs, and on final students’ evaluation.