Biopolymers, such as proteins and RNA, are integral components of living organisms and have evolved through a process of repeated mutation and selection. The technique of "cell-free in vitro evolution" is a powerful experimental approach for developing biopolymers with desired functions and structural properties. Since Spiegelman's pioneering work over 50 years ago, biopolymers with a wide range of functions have been developed using in vitro evolution in cell-free systems. The use of cell-free systems offers several advantages, including the ability to synthesize a wider range of proteins without the limitations imposed by cytotoxicity, and the capacity for higher throughput and larger library sizes than cell-based evolutionary experiments. In this chapter, we provide a comprehensive overview of the progress made in the field of cell-free in vitro evolution by categorizing evolution into directed and undirected. The biopolymers produced by these methods are valuable assets in medicine and industry, and as a means of exploring the potential of biopolymers.