An information-theoretic framework for unequal error protection is developed in terms of the exponential error bounds. The fundamental difference between the bit-wise and message-wise unequal error protection (UEP) is demonstrated, for fixed-length block codes on discrete memoryless channels (DMCs) without feedback. Effect of feedback is investigated via variable-length block codes. It is shown that, feedback results in a significant improvement in both bit-wise and message-wise UEPs (except the single message case for missed detection). The distinction between false-alarm and missed-detection formalizations for message-wise UEP is also considered. All results presented are at rates close to capacity.