The formation and study of molecules that model the sp-hybridized carbon allotrope, carbyne, is a challenging field of synthetic physical organic chemistry. The target molecules, oligo- and polyynes, are often the preferred candidates as models for carbyne because they can be formed with monodisperse lengths as well as defined structures. Despite a simple linear structure, the synthesis of polyynes is often far from straightforward, due in large part to a highly conjugated framework that can render both precursors and products highly reactive, i.e., kinetically unstable. The vast majority of polyynes are formed as symmetrical products from terminal alkynes as precursors via an oxidative, acetylenic homocoupling reaction based on the Glaser, Eglinton-Galbraith, and Hay reactions. These reactions are very efficient for the synthesis of shorter polyynes (e.g., hexaynes and octaynes), but yields often drop dramatically as a function of length for longer derivatives, usually starting with the formation of decaynes. The most effective approach to circumvent unstable precursors and products has been through the incorporation of sterically demanding end groups that serve to "protect" the polyyne skeleton. This approach was arguably identified in the early 1950s by Bohlmann and co-workers with the synthesis of tBu-end-capped polyynes. During the next 50 years, a polyyne with 14 contiguous alkyne units remained the longest isolated derivative until 2010, when the record was extended to 22 alkyne units. The record length was broken again in 2020, when a polyyne consisting of 24 alkynes was isolated and characterized. Beyond polyynes, there have been several reports describing the potential synthesis of carbyne, but conclusive characterization and proof of structure have been tenuous. The sole example of synthetic carbyne arises from synthesis within carbon nanotubes, when chains of thousands of sp carbon atoms have been linked to form polydisperse samples of carbyne. Thus, model compounds for carbyne, the polyynes, remain the best means to examine and predict the experimental structure and properties of this carbon allotrope.This Account will discuss the general synthesis of polyynes using homologous series of polyynes with up to 10 alkyne units as examples (decaynes). The limited number of specific syntheses of series with longer polyynes will then be presented and discussed in more detail based on end groups. The monodisperse polyynes produced from these synthetic efforts are then examined toward providing our best extrapolations for the expected characteristics for carbyne based on 13C NMR spectroscopy, UV-vis spectroscopy, X-ray crystallography, and Raman spectroscopy.