This invited talk will review a series of our recent studies on high-entropy ceramics (HECs) and compositionally complex ceramics (CCCs) and discuss the future perspective. Various single-phase equimolar quinary (five-component) HECs, e.g., MB2, MB, M3B4, MB4, and MB6 borides, MSi2 and M3Si5 silicides, perovskite, fluorite, and pyrochlore oxides, and (intermetallic) aluminides have been fabricated. We further proposed to extend HECs to CCCs to include non-equimolar compositions and further consider short- and long-range orders, which reduce configurational entropies but offer additional dimensions and opportunities to tailor and improve various properties. We also reported the first dual-phase HECs/CCCs. Using compositionally complex fluorite-based oxides (CCFBOs, which can possess fluorite or defect fluorite, pyrochlore, weberite, fergusonite, and bixbyite phases) as the model systems, we have recently discovered long- and short- range orders, composition- and redox-induced order-disorder transitions (ODTs), and ultrahigh-entropy weberite and fergusonite phases in several 10- to 21-component systems.