Bose-Einstein condensates (BECs) provide an ideal platform for exploring novel quantum states (QTs) in synthetic spin-orbit coupling (SOC). In article number 2500431, Yun Liu and Zu-Jian Ying analyse the interplay of SOC with other interactions and potential geometry by BECs in concentric annular traps. Various exotic QTs emerge, including facial-makeup states, fissure states, stripe states, half-disk states, half-skyrmion fence, etc. Peculiar density-phase separation is noticed. The study illustrates manipulations of exotic QTs and supplies abundant quantum resources for potential applications.