In modern spintronics properties of non-equilibrium orbital polarization and orbital currents start to attract significant attention. In this talk we will review the theory of orbital magnetism in low-symmetric crystals and corresponding current-induced orbital magnetization. We will in particular show that applied electrical currents and optical pulses can drive non-equilibrium orbital magnetism and currents of orbital angular momentum. These orbital currents can be used to transmit angular momentum over large distances in solids, and can be utilized to exert sizeable orbital torques on magnetization thus enabling magnetic switching even in light materials with weak spin-orbit interaction. Moreover, we will underline that in fluctuating magnets spin excitations can mediate a significant orbital response which can be coupled to temperature gradients so as to ignite thermal orbital currents. We will thus attempt to promote a paradigm that unleashing non-equilibrium orbital physics and entanglement of spin and orbital degrees of freedom in diverse classes of materials can lead to much richer physics than previously expected, and might provide a key to realization of novel properties of matter out of equilibrium as well as energy-efficient applications.