DNA computing is recognized as one of the most outstanding candidates of next-generation molecular computers that perform Boolean logic using DNAs as basic elements. Benefiting from DNAs' inherent merits of low-cost, easy-synthesis, excellent biocompatibility, and high programmability, DNA computing has evoked substantial interests and gained burgeoning advancements in recent decades, and also exhibited amazing magic in smart bio-applications. In this review, recent achievements of DNA logic computing systems using multifarious materials as building blocks are summarized. Initially, the operating principles and functions of different logic devices (common logic gates, advanced arithmetic and non-arithmetic logic devices, versatile logic library, etc.) are elaborated. Afterward, state-of-the-art DNA computing systems based on diverse "toolbox" materials, including typical functional DNA motifs (aptamer, metal-ion dependent DNAzyme, G-quadruplex, i-motif, triplex, etc.), DNA tool-enzymes, non-DNA biomaterials (natural enzyme, protein, antibody), nanomaterials (AuNPs, magnetic beads, graphene oxide, polydopamine nanoparticles, carbon nanotubes, DNA-templated nanoclusters, upconversion nanoparticles, quantum dots, etc.) or polymers, 2D/3D DNA nanostructures (circular/interlocked DNA, DNA tetrahedron/polyhedron, DNA origami, etc.) are reviewed. The smart bio-applications of DNA computing to the fields of intelligent analysis/diagnosis, cell imaging/therapy, amongst others, are further outlined. More importantly, current "Achilles' heels" and challenges are discussed, and future promising directions of this field are also recommended.