All undergraduates in physics and astronomy should have access to significant research experiences. When given the opportunity to tackle challenging open-ended problems outside the classroom, students build their problem-solving skills in ways that better prepare them for the workplace or future research in graduate school. Accelerator-based research on fundamental nuclear and particle physics can provide a myriad of opportunities for undergraduate involvement in hardware and software development as well as “big data” analysis. The collaborative nature of large experiments exposes students to scientists of every culture and helps them begin to build their professional network even before they graduate. This paper presents an overview of my experiences - the good, the bad, and the ugly - engaging undergraduates in particle and nuclear physics research at the CERN Large Hadron Collider and the Los Alamos Neutron Science Center.