This invention is directed generally to substituted pyrimidinone compounds that generally inhibit p38 kinase, TNF, and/or cyclooxygenase activity. Such substituted pyrimidinone include compounds generally corresponding in structure to the following formula (I): wherein R1, R2, R3, R4A, R4B, R4C, R4D and R4E are as defined in this specification. This invention also is directed to compositions of such substituted pyrimidinones (particularly pharmaceutical compositions), intermediates for the syntheses of such substituted pyrimidinones, methods for making such substituted pyrimidinones, and methods for treating (including preventing) conditions (typically pathological conditions) associated with p38 kinase activity, TNF activity, and/or cyclooxygenase-2 activity.