There are three popular styles: rimless frames, half-rim frames and full-rimmed frames.
The biggest benefit of rimless eyeglasses is that there are no frames to obstruct one’s view, thereby expanding the field of vision. Rimless frames are extremely lightweight, which makes them more comfortable than a regular frame. Made from materials like titanium, stainless steel, aluminium, etc. you may even forget you're wearing glasses.
Half-rim frames only feature a frame on the top half of the eyeglasses and the lens is open on the bottom with a filament string keeping them in place. Half-rim glasses have become increasingly popular in the last decade and elicit a very contemporary look. It may not be suitable for people who have a thicker lens may which may not fare well with these frames in the long run.
Full-rim frame is a very broad term given to any type of eyeglasses that feature a frame that completely wraps around the lenses. They come in various materials, sizes, colours and shapes. Thick, big, full-rimmed glasses are currently in vogue.