Abstract: Scale-free networks and related concepts including power-law distribution and preferential attachment mechanism are core concepts in network science. Researches on these concepts have a long history, but there are still some debates by now. The paper aims at reveal the links among some important historic researches on these concepts from a network perspective, including reveal the fundamental works of Price that had been neglected for a long time. This paper introduces and discusses some controversial issues on these concepts, including quarrels between Simon and Mandelbrot around mechanisms for power law in the middle of 20th century, and recently debates on whether scale-free networks are rich or rare. Finally, the paper discusses future researches on scale-free networks.