Telomerase is a DNA polymerase that extends the 3' ends of chromosomes by processively synthesizing multiple telomeric repeats. It is a unique ribonucleoprotein (RNP) containing a specialized telomerase reverse transcriptase (TERT) and telomerase RNA (TER) with its own template and other elements required with TERT for activity (catalytic core), as well as species-specific TER-binding proteins important for biogenesis and assembly (core RNP); other proteins bind telomerase transiently or constitutively to allow association of telomerase and other proteins with telomere ends for regulation of DNA synthesis. Here we describe how nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography of TER and protein domains helped define the structure and function of the core RNP, laying the groundwork for interpreting negative-stain and cryo electron microscopy (cryo-EM) density maps of Tetrahymena thermophila and human telomerase holoenzymes. As the resolution has improved from ∼30 Å to ∼5 Å, these studies have provided increasingly detailed information on telomerase architecture and mechanism.