Infrared spectra from the Spitzer Space Telescope trace the evolution of carbon-rich dust from the asymptotic giant branch (AGB) to young planetary nebulae (PNe). On the AGB, amorphous carbon dominates the dust, but SiC and MgS also appear. In more evolved systems with warmer central stars, the spectra reveal the unidentified 21 μm feature, features from aliphatic hydrocarbons, and spectra from polycyclic aromatic hydrocarbons (PAHs), often with shifted feature positions indicative of the presence of aliphatics. More evolved systems with hot central stars show more typical PAH spectra, along with fullerenes and/or an emission feature known as the big-11 feature at ~11 μm. This features arises from a combination of SiC and PAHs, and it is usually accompanied by a shoulder at 18 μm, which while unidentified might be from cool silicate grains. The strong emission from MgS and SiC in young PNe probably arises from coatings on carbonaceous grains.