Itinerant ferromagnetism (FM) is intrinsically a strongly correlated phenomenon, which remains a major challenge of condensed matter physics. Most FM materials are orbital-active with prominent Hund’s coupling. However, the local physics of Hund’s rule usually does not lead to the FM long-range order. Furthermore, the magnetic phase transitions of itinerant electrons are also long-standing problems difficult to handle by using perturbative methods. In this talk, I will present non-perturbative studies on itinerant FM. Exact theorems are established for a stable itinerant FM phase in a large region of electron densities in multi-orbital systems, which provide sufficient conditions for Hund’s rule to build up global FM coherence. In addition, thermodynamic properties and magnetic phase transitions of itinerant electrons are studied via sign-problem-free quantum Monte Carlo simulations at generic fillings. Without introducing local moments as a priori, the Curie-Weiss metal behavior is identified in a wide range of temperatures. These results will provide important guidance to the current experimental search for novel itinerant FM states in a large class of systems ranging from the transition-metal-oxide heterostructures (e.g. LaAlO3/SrTiO3) to the p-orbital bands in optical lattices filled with ultra-cold fermions.