Every real number can be expressed as a simple continued fraction. In particular, a number is rational if and only if its simple continued fraction has a finite number of terms. Owing to this property, continued fractions have been a powerful tool which determines a real number to be rational or not. Continued fractions provide not only a series of best estimate for a real number, but also a useful method for finding near commensurabilities between events with different periods. In this paper, we investigate the history and some properties of continued fractions, and then consider their applications in several examples. Also we explain why the Fibonacci numbers and the Golden section appear in nature in terms of continued fractions, with some examples such as the arrangements of petals round a flower, leaves round branches and seeds on seed head.