The present disclosure provides aldehyde-tagged immunoglobulin (Ig) polypeptides that can be converted by a formylglycine-generating enzyme to produce a 2-formylglycine (FGly)-modified Ig polypeptide. An FGly-modified Ig polypeptide can be covalently and site-specifically bound to a moiety of interest to provide an Ig conjugate. The disclosure also encompasses methods of production of such aldehyde-tagged Ig polypeptides, FGly-modified Ig polypeptides, and Ig conjugates, as well as methods of use of same.