Many people in the U.S. and Europe use hair dyes. It is estimated that more than one-third of women over age 18 and about 10 percent of men over age 40 use some type of hair dye. Modern hair dyes are classified as permanent, semi permanent, and temporary. Permanent hair dyes, which make up about 80 percent of the market, consist of colorless dye "intermediates" and dye "couplers." In the presence of hydrogen peroxide, the intermediates and couplers react to form pigment molecules. Darker colors are formed by using higher concentrations of intermediates. Semi permanent and temporary hair dyes are nonoxidative and include colored compounds that stain hair directly.
Over 5,000 different chemicals are used in hair dye products, some of which are reported to be carcinogenic in animals. Because so many people use hair dyes, scientists have tried to determine whether exposure to the chemicals in hair coloring products is associated with an increased risk of cancer in people.
Early hair dye formulations contained chemicals, including aromatic amines that were found to cause cancer in animals. In the mid- to late 1970s, however, manufacturers changed the components in dye products to eliminate some of these chemicals. It is not known whether some of the chemicals still used in hair dyes can cause cancer. Given the widespread use of hair dye products, even a small increase in risk may have a considerable public health impact.
Over the years, some epidemiologic studies have found an increased risk of bladder cancer in hairdressers and barbers. A 2008 report of the Working Group of the International Agency for Research on Cancer (IARC) concluded that some of the chemicals these workers are exposed to occupationally are "probably carcinogenic to humans".
Although some studies have linked the personal use of hair dyes with increased risks of certain cancers of the blood and bone marrow, such as non-Hodgkin lymphoma and leukemia, other studies have not shown such links. Studies of breast and bladder cancer have also produced conflicting results. Relatively few studies have been published about the association of hair dye use with the risk of other cancers. Based on its review of the evidence, IARC concluded that personal use of hair dyes is "not classifiable as to its carcinogenicity to humans".
This answer is based on source information from the National Cancer Institute.