Recent advances in genome projects and adjacent areas of bioinformatics and structural genomics intesified research efforts in protein structure comparison, classification, and prediction. Many algorithms used in this research rely on analysis of patterns in nearest-neighbor residue arrangements in three-dimensional protein structures. One of the most robust and efficient methods for neighbor identification is the Delaunay tessellation - a computational geometry algorithm that can be used to define all sets of four natural neighbor residues in proteins. Statistical analysis of compositional and geometrical patterns in the sets of nearest neighbor residues helps facilitate understanding and interpretation of structure-sequence and structure-function correlations in proteins. Examples of applications discussed in this presentation include topologically-based measurement of protein structure similarity, secondary structure assignment, active site identification, and computational mutagenesis.