  We briefly review the recent progress of theories and experiments on
spin-orbital-angular-momentum (SOAM)-coupled quantum gases. The coupling
between the intrinsic degree of freedom of particles and their external orbital
motions widely exists in universe, and leads to a broad variety of fundamental
phenomena both in the classical physics and quantum mechanics. Recent
realization of synthetic SOAM coupling in cold atoms has attracted a great deal
of attention, and stimulates a large amount of considerations on exotic quantum
phases in both Bose and Fermi gases. In this review, we present a basic idea of
engineering SOAM coupling in neutral atoms, starting from a semiclassical
description of atom-light interaction. Unique features of the single-particle
physics in the presence of SOAM coupling are discussed. The intriguing
ground-state quantum phases of weakly interacting Bose gases are introduced,
with emphasis on a so-called angular stripe phase, which has yet been observed
at present. It is demonstrated how to generate a stable giant vortex in a
SOAM-coupled Fermi superfluid. We also discuss topological characters of a
Fermi superfluid in the presence of SOAM coupling. We then introduce the
experimental achievement of SOAM coupling in $^{87}$Rb Bose gases and its first
observation of phase transitions. The most recent development of SOAM-coupled
Bose gases in experiments is also summarized. Regarding the controllability of
ultracold quantum gases, it opens a new era, on the quantum simulation point of
view, to study the fundamental physics resulted from SOAM coupling as well as
newly emergent quantum phases.
