Today the applications of nuclear physics span a very broad range of topics and fields. This review discusses a number of aspects of these applications, including selected topics and concepts in nuclear reactor physics, nuclear fusion, nuclear non--proliferation, nuclear--geophysics, and nuclear medicine. The review begins with a historic summary of the early years in applied nuclear physics, with an emphasis on the huge developments that took place around the time of World War II, and that underlie the physics involved in designs of nuclear explosions, controlled nuclear energy, and nuclear fusion. The review then moves to focus on modern applications of these concepts, including the basic concepts and diagnostics developed for the forensics of nuclear explosions, the nuclear diagnostics at the National Ignition Facility, nuclear reactor safeguards, and the detection of nuclear material production and trafficking. The review also summarizes recent developments in nuclear geophysics and nuclear medicine. The nuclear geophysics areas discussed include geo--chronology, nuclear logging for industry, the Oklo reactor, and geo--neutrinos. The section on nuclear medicine summarizes the critical advances in nuclear imaging, including PET and SPECT imaging, targeted radionuclide therapy, and the nuclear physics of medical isotope production. Each subfield discussed requires a review article onto itself, which is not the intention of the current review. Rather, the current review is intended for readers who wish to get a broad understanding of applied nuclear physics.