A drain stopper includes a cap, a seal and a strainer engaged with the cap, and a gripping element engaged with the strainer. The gripping element is resilient and has a generally tubular shape with longitudinal notches, which give it a segmented annular shape. A person grips and squeezes the gripping element to insert the stopper/strainer into a drain pipe, after which the gripping element expands and grips an inside wall of the drain pipe. The person pushes downwardly on the cap to place the stopper/strainer in a closed position and pulls up on the cap for an open position. Another drain stopper includes a cap, a seal, a push-push mechanism, a strainer engaged with the mechanism, and a flange or prongs that rest on a drain flange for holding and supporting the drain stopper.