1. Literally, to smile at someone or something in a smug, scornful, or condescending manner. Sarah just smirked at me when I invited her to my party. My dad sat on the porch smirking at me as I made a hash of repairing the engine by myself.

2. By extension, to regard someone or something with smugness, scorn, condescension, etc. I feel like the rest of the world smirks at us because of our outdated, backwards laws. I used to smirk at the idea of working in a cubicle for eight hours a day, but once I had kids and needed steady income, it stopped sounding so unappealing.