Lindsay Lecture

Cosmic X-ray astronomy has flourished in the nearly half century since the discovery of Scorpius X-1. Through most of that history, the primary advances came through continual improvements in imaging, timing and collecting area. Cosmic X-ray spectroscopy also progressed, albeit more slowly, reaching maturity only in the past decade with Chandra and XMM-Newton. This talk will review the challenges presented by the laws of physics to building high resolution, high throughput X-ray spectrometers and how they have been overcome. The development of the High Energy Transmission Grating Spectrometer for Chandra, with resolving powers of 1000 and reasonable sensitivity, is a case in point. Emission and absorption line spectroscopy is now revealing a wealth of detailed astrophysical information about virtually every class of X-ray source, as well as interstellar and intergalactic matter. I will review some of the highlights and prospects for the future.