Intraflagellar transport (IFT) trains are molecular machines that traffic proteins between cilia and the cell body. With a molecular weight over 80 MDa, each IFT train is a dynamic polymer of two large complexes (IFT-A and -B) and motor proteins, posing a formidable challenge to mechanistic understanding. Here, we reconstituted the complete human IFT-A complex and obtained its structure using cryo-EM. Combined with AlphaFold prediction and genome-editing studies, our results illuminate how IFT-A polymerizes; interacts with IFT-B; and uses an array of beta-propeller and TPR domains to create "carriages" of the IFT train that engage TULP adaptor proteins. We show that IFT-A:TULP carriages are essential for cilia localization of diverse membrane proteins, as well as ICK - the key kinase regulating IFT train turnaround. These data establish a structural link between IFT-A's distinct functions, provide a blueprint for the IFT-A train, and shed light on how IFT evolved from a proto-coatomer ancestor.