Semi-rimless frames are preferred by many eyeglass wearers today because they provide a less-noticeable rim and are softer on the face. As Optics Place.com notes, "Partially-rimless eyeglasses are lightweight, very fashionable and almost invisible" (See Reference 1). Traditional glasses have an obvious frame that extends around the entirety of the eye and face where as semi-rimless frames contain a nearly invisible plastic line that holds the bottom portion of the lenses in place. Most consumers don't know that most retail pairs of semi-rimless frames use a thin fishing line to buttress the lower portion of the lenses. Therefore, its conceivable that someone could repair or reinsert them on their own.
Determine whether your actual frame is broken or the plastic line is just loose or broken. If neither is the case and your lens has just popped out, you can easily reinsert it. A broken frame and possibly a broken plastic line will require assistance from an eyeglass shop.
Slide the upper portion of the lens up against the frame and hold it in place. Stretch the plastic line around the bottom of the lens and into the lens groove carefully with your other hand without scratching the lens.
Stretch the line a bit if it's too tight. For lines with slack, simply hold them about four to six inches above a small amount of heat like a stove turned on low. The heat will shrink the plastic slightly after it's exposed.
Replace the plastic fishing line if you feel comfortable attempting the job. Grip the line with a pair of pliers and pull until both ends come loose from the frame.
Measure out a similar piece of fishing line that is slightly longer. Thread it around the frame in the grooves and through both ends of the frame. Leave some slack.
Cut off excess line hanging from the outer portion. Put the lens in place, and shrink the line using heat. The line should shrink to fit the lens after heat is applied.