In the last 15 years, \({\sim }\) 20 giant exoplanets have been directly imaged in the infrared as companions to young stars. With photometry and spectroscopy of these planets from ground-based extreme coronagraphic instruments and interferometers (SPHERE and GRAVITY at VLT, GPI at Gemini, KPIC at Keck, and CHARIS at Subaru) and using JWST from space, we are beginning to characterize and classify the atmospheres of these objects. Initially, it was assumed that young planets would be similar to field brown dwarfs, more massive objects that nonetheless share similar effective temperatures and compositions. Surprisingly, young planets appear considerably redder than field brown dwarfs, likely a result of their low surface gravities and indicating much different atmospheric structures. Some of them are displaying emission lines indicative of active accretion and of a mass reservoir in their vicinity. Preliminarily, young free-floating planets appear to be as or more variable than field brown dwarfs, due to rotational modulation of inhomogeneous top-of-atmosphere features. Direct-imaging spectroscopy of giant exoplanets now is a prelude for the study of habitable zone planets. Direct-imaging spectroscopy of a large sample of habitable zone planets with future telescopes such as the Habitable Worlds Observatory will be necessary to identify multiple biosignatures and establish habitability for Earth-mass exoplanets in the habitable zones of nearby solar-mass stars.