  With the advances in high resolution and spin-resolved scanning tunneling
microscopy as well as atomic-scale manipulation, it has become possible to
create and characterize quantum states of matter bottom-up, atom-by-atom. This
is largely based on controlling the particle- or wave-like nature of electrons,
as well as the interactions between spins, electrons, and orbitals and their
interplay with structure and dimensionality. We review the recent advances in
creating artificial electronic and spin lattices that lead to various exotic
quantum phases of matter, ranging from topological Dirac dispersion to complex
magnetic order. We also project future perspectives in non-equilibrium
dynamics, prototype technologies, engineered quantum phase transitions and
topology, as well as the evolution of complexity from simplicity in this newly
developing field.
