In recent years, both fields of physics and psychology have made important scientific advances. The emergence of new instruments gave rise to a data-driven neuroscience allowing us to learn about the state of the brain supporting known mental functions and conversely. In parallel, the appearance of new mathematics allowed the development of computational models describing fundamental brain functions and implementing them in technological applications. While emphasizing the methodology of physics, the special issue aims to bring together these trends in both the experimental and theoretical sciences in order to explain some of the most basic mental processes such as perception, cognition, emotion, consciousness, and learning. In this editorial, we define unsolved problems for brain and psychological sciences, discuss possible means toward their respective solutions, and outline some collaborative initiatives aiming toward these goals. The following problems are defined in gradual order of difficulty: what are the universal properties of human behavior across conditions and cultures? What have each culture learned over historical times and why should specific elements of knowledge be accumulated over cultural evolution? Can computational psychiatry help predict, understand, and cure mental disorders? What is the function of art and cultural artifacts such as music, fiction, or poetry for the cognitive system? How to explain the relation between first-person subjective experience and third-person objective physiological data? What neural mechanisms operate on which mental content at the highest levels of organization of the hierarchical brain? How do abstract ideas emerge from sensory-motor contingencies and what are the conditions for the birth of a new concept? Could symmetry play a role in psychogenesis and support the emergence of new hierarchical layers in cognition? How can we start addressing the question of meaning scientifically, and what does it entail for the physical sciences?