The new spectroscopic technique of photoassociation of ultracold atoms is reviewed, with an emphasis on connecting this area to traditional bound-state molecular spectroscopy. In particular, in contrast to photoassociative spectra at thermal energies, which are broad and of low information content, photoassociative spectra of ultracold atoms are high resolution, permitting observation of small vibrational and rotational spacings of long-range molecular levels near dissociation (typically with outer classical turning points >20 Å). The types of detection and theoretical analysis employed are illustrated, primarily using the example of 39K2. Future directions and applications of this field (e.g., to ultracold molecular formation) are also discussed. Copyright 1999 Academic Press.