The most common type of protein secondary structure after the alpha helix and beta sheet is the four-residue beta turn, which plays many key structural and functional roles. Existing tools for the study of beta turns operate in backbone dihedral-angle (Ramachandran) space, which presents challenges for the visualization, comparison and analysis of the wide range of turn conformations. In this work, a new turn-local coordinate system and structural alignment, together with a set of geometric descriptors for turn backbone shape, are incorporated into ExploreTurns, a web facility for the exploration, analysis, geometric tuning and retrieval of beta turns and their contexts which combines the advantages of Ramachandran- and Euclidean-space representations. Due to the prevalence of beta turns in proteins, this facility, supported by its interpreter for a new general nomenclature which classifies H-bonded loop motifs and beta hairpins, serves as an exploratory browser and analysis tool for most loop structure. The tool is applied to the detection of new H-bonded loops, including short and "double" Schellman loops, a large family of beta-bulge loops with a range of geometries and H-bond topologies, and other motifs. Other applications presented here include the mapping of sequence preferences in Asx helix N-caps and an investigation of the depth dependence of beta-turn geometry. ExploreTurns, available at www.betaturn.com, should prove useful in research, education, and applications such as protein design, in which an enhanced Euclidean-space picture of turn and motif structure and the ability to identify and tune structures suited to particular requirements may improve performance.