Carbon chains or carbyne-like structures represent the next generation of 1D materials whose properties can be tuned by the chain length, doping, and the type of termination. Currently inaccessible technology of the macroscopic carbyne synthesis and characterization makes theoretical work especially valuable. The state of the art methods being applied in the field are density functional theory and molecular dynamics. This paper provides a review of the current state of research on modeling linear carbon structures and related materials. We show that even though the “static” properties of carbon chains (mechanical strength, thermal conduction, band gaps, and phonon spectra) are extensively described, there are only a few simulations of the synthesis processes that constitute the next challenge in 1D research.