Quantum measurement problem is a long-standing problem at the heart of the foundations of modern physics and nascent technology, such as quantum technology. The last forty years brought a renowned interest in this problem with an emphasis on the new foundations of quantum theory and unpredicted formulation of some new quantum disciplines, such as the open quantum systems theory and the quantum information and computation science. A state of the art of the problem of measurement is shortly presented, including a brief historical view, with a review of the authors' original contributions.