This review provides a discussion of the current state of research on linear carbon structures and related materials based on sp-hybridization of carbon atoms ( polyynes and cumulenes). We show that such systems have widely tunable properties and thus represent an intriguing and mostly unexplored field for both fundamental and applied sciences. We discuss the rich interplay between the structural, vibrational, and electronic properties focusing on recent advances and the future perspectives of carbon-atom wires and novel hybrid sp-sp 2 -carbon architectures.