We give a brief overview on some recent progress in quark pairings in dense
quark/nuclear matter mostly developed in the past five years. We focus on
following aspects in particular: the BCS-BEC crossover in the CSC phase, the
baryon formation and dissociation in dense quark/nuclear matter, the
Ginzburg-Landau theory for three-flavor dense matter with UA​(1) anomaly,
and the collective and Nambu-Goldstone modes for the spin-one CSC.Comment: RevTex 4, 25 pages, 9 figures, presented for the KITPC (Kavli
Institute for Theoretical Physics China) program "AdS/CFT and Novel
Approaches to Hadron and Heavy Ion Physics' in Oct. 11- Dec. 3, 201