The present invention provides engineered polypeptide conjugates (e.g., antibody-drug-conjugates, toxin-(biocompatible polymer) conjugates, antibody-(biocompatible polymer) conjugates, and bispecific antibodies) comprising acyl donor glutamine-containing tags and amine donor agents. In one aspect, the invention provides an engineered Fc-containing polypeptide conjugate comprising the formula (Fc-containing polypeptide)-T-A, wherein T is an acyl donor glutamine-containing tag engineered at a specific site or comprises an endogenous glutamine made reactive by the Fc-containing polypeptide engineering, wherein A is an amine donor agent, and wherein the amine donor agent is site-specifically conjugated to the acyl donor glutamine-containing tag or the endogenous glutamine. The invention also provides methods of making engineered polypeptide conjugates using transglutaminase.