  In solids, electronic Bloch states are formed by atomic orbitals. While it is
natural to expect that orbital composition and information about Bloch states
can be manipulated and transported, in analogy to the spin degree of freedom
extensively studied in past decades, it has been assumed that orbital quenching
by the crystal field prevents significant dynamics of orbital degrees of
freedom. However, recent studies reveal that an orbital current, given by the
flow of electrons with a finite orbital angular momentum, can be electrically
generated and transported in wide classes of materials despite the effect of
orbital quenching in the ground state. Orbital currents also play a fundamental
role in the mechanisms of other transport phenomena such as spin Hall effect
and valley Hall effect. Most importantly, it has been proposed that orbital
currents can be used to induce magnetization dynamics, which is one of the most
pivotal and explored aspects of magnetism. Here, we give an overview of recent
progress and the current status of research on orbital currents. We review
proposed physical mechanisms for generating orbital currents and discuss
candidate materials where orbital currents are manifest. We review recent
experiments on orbital current generation and transport and discuss various
experimental methods to quantify this elusive object at the heart of
$orbitronics$ $-$ an area which exploits the orbital degree of freedom as an
information carrier in solid-state devices.
