Mutations in the telomerase complex disrupt either nucleic acid binding or catalysis, and are the cause of numerous human diseases. Despite its importance, the structure of the human telomerase complex has not been observed crystallographically, nor are its dynamics understood in detail. Fragments of this complex from Tetrahymena thermophila and Tribolium castaneum have been crystallized. Biochemical probes provide important insight into dynamics. In this work we present evidence that the T. castaneum structure is Telomerase Reverse Transcriptase, addressing a topic of current debate. We use this structure to build a partial model of the human Telomerase complex. The model suggests an explanation for the structural basis of several disease-associated mutations. We then generate a 3D kinematic trajectory of telomere elongation following a “typewriter” mechanism: the RNA template moves to keep the end of the growing telomere in the active site, disengaging after every 6-residue extension to execute a “carriage return” and go back to its starting position. A hairpin can easily form in the telomere, from DNA residues leaving the telomere-template duplex. The trajectory is consistent with available experimental evidence and can be validated with focused biochemical experiments.