We briefly review recent advances in theory and experiment on spin-orbit angular momentum (SOAM) coupled quantum gases. The coupling of the intrinsic degrees of freedom of particles and their external orbital motion is widespread in the universe and leads to various fundamental phenomena in both classical and quantum mechanics. Recent realizations of synthetic SOAM coupling in cold atoms have received a great deal of attention and have stimulated many considerations on exotic quantum phases in both Bose and Fermi gases. In this review, we present the basic ideas of his engineering of SOAM bonds in neutral atoms, starting with a semi-classical description of the interaction of atoms and light. We describe a unique feature of single-particle physics in the presence of SOAM coupling. Intriguing ground-state quantum phases of weakly interacting Bose gases are introduced, with emphasis on the so-called angular-stripe phases, which are currently unobserved. A method to generate stable giant vortices in SOAM-coupled Fermi superfluids is shown. We also describe the topological properties of Fermi superfluids in the presence of SOAM coupling. Next, we present his experimental results of SOAM coupling in $^{87}$Rb Bose gas and the first observation of the phase transition. The latest developments in SOAM-coupled Bose gases in experiments are also summarized. Regarding the controllability of ultra-low temperature quantum gases, a new era opens up in terms of quantum simulations to study the fundamental physics arising from SOAM coupling and emerging quantum phases.
