This review describes a program that we have conducted for more than 20 years, first at the University of South Florida and then at the University of Maryland Center for Environmental Science, to systematically measure stability constants for solution complexes of yttrium and all rare earth elements (YREE), except Pm, at the ionic strength of seawater (I ~ 0.7). This effort informs our goal of better characterizing and understanding YREE speciation in the marine environment, in the presence of both inorganic and organic ligands (and sorbents). Since all YREE appear to show similar behavior as a function of ionic strength, patterns of stability constants for individual ligands have been extrapolated to I = 0 whenever sufficient data for at least one member of the series are available. Complexes with hydroxide, fluoride and chloride, carbonate, and sulfate, are treated in detail, being the most prominent inorganic YREE ligands. A natural siderophore (DFOB) and synthetic polyaminopolycarboxylic acids (NTA, EDTA, DTPA) are given as examples of strong organic YREE complexation which, while remaining poorly quantified, is thought to be important. Several YREE ligands that play a negligible role in seawater, or for which data are as yet scarce, are also briefly discussed. Many different and sometimes novel analytical approaches were used in our experiments and these are summarized in the introductory sections, along with a primer on the theory of chemical speciation. This paper is intended as a retrospective of our work, not as a critical review of all available data. Literature values are thus cited primarily for comparison with our results, to support specific arguments, or to highlight prior discrepancies that prompted our own studies.