Line, though a formal factor in the analysis of any and all art, is important in life too. It can represent boundaries, goals as well as more solid things such as a simple profile. The arts have always used it many different ways. In my opinion, the modern abstract movement sweeping through visual arts has made it rather more arbitrary. It has always been interesting to me, as a valuable and flexible part of any composition. Unfortunately, I have never been able to do very much significant work with it but my sketchbooks are full of simply line drawings, cross hatching, and shapes. Having said that, here's my recent work with line. I loved doing it and hope to further develop these.
I suppose these can be called self portraits, but to be honest, I used photographs of myself as references. They were definitely not meant to be self-portraits.
The above picture is a detail of one of the pieces. I included it just to show the shapes created by the lines. I found these interesting and strived to create them in the above pieces.