Pyrrolo-pyridine, pyrrolo-pyrimidine and related heterocyclic compounds analogues of the formula: wherein R, R2, R5, E, Z1, Z3, Z4, and Ar are defined herein. Such compounds are ligands of C5a receptors. Preferred pyrrolo-pyridine, pyrrolo-pyrimidine and related heterocyclic compounds of the invention bind to C5a receptors with high affinity and exhibit neutral antagonist or inverse agonist activity at C5a receptors. The present invention also relates to pharmaceutical compositions comprising such compounds, and to the use of such compounds in treating a variety of inflammatory, cardiovascular, and immune system disorders. In addition, the present invention provides labeled pyrrolo-pyridine, pyrrolo-pyrimidine and related heterocyclic compounds, which are useful as probes for the localization of C5a receptors.