Traditional financial theories was based on the normal distribution of the price increments and discussed the probability density function (PDF) of the increments in a given time scale. Recent researches show that the tail of the PDF of the increments was fatter than the normal distribution. For describing the fat tail distribution and discussing the similarity among PDFs at different time scales, scientists introduced the Lévy stable distribution to describe the price increments. Because the Lévy stable distribution has too fattai1．the truncated LEvy stable distribution has been introduced．The truncated Levy stable distribution overcomes the shortcoming of the Levy stable distribution．The discovery of the multiscale behavior in the financial markets is a great progress and has important significance in the theory and practice．This paper review the new researches for the scaling and scale invariance in financia1 markets．