Isoflavones and cancer
Because Asians, who consume high quantities of soy and soy isoflavones, have a lower risk of hormone-related cancer, such as breast cancer and prostate cancer, many studies have investigated the link between isoflavones intake and this risk. Unfortunately the results of these studies are not always conclusive and sometimes conflicting. Some in vitro experiments and animal studies using high levels of isoflavones demonstrate a tumor-promoting effect of isoflavones, but epidemiological studies generally show that soy isoflavones are safe and actually reduce cancer risks.
Estrogenic and anti-estrogenic effect of isoflavones
It is well established that the female hormone estrogen increases the risk of certain cancers, the so-called hormone-related cancers, such as breast cancer and prostate cancer. But what is the effect of isoflavones with structures similar to that of estrogen? Human cells contain two types of estrogen receptors (places that bind to estrogen and result in activation): estrogen receptor alpha (ER-A) and estrogen receptor beta (ER-B). Binding of estrogen to ER-A results in cell growth and carcinogenicity in estrogen-sensitive tissue, whereas binding to ER-B results in an opposite reaction. Soy isoflavones and their metabolite equol show a higher affinity for ER-B, whereas the binding capacities for red clover isoflavones are less conclusive 
Scientists believe that isoflavones may exert estrogenic or anti-estrogenic action depending on the level of estradiol in the blood. In premenopausal women, having high levels of circulating estradiol, isoflavones may act as anti-estrogens, whereas in postmenopausal women, with low levels of circulating estradiol, they may have estrogen-like activities. Animal studies demonstrated that isoflavones may promote breast cancer growth, but human data do not confirm these concerns. Soy foods have been part of the diet in many Asian countries for centuries and are generally considered as safe and healthy. On the other hand, the safety of isoflavones supplements, containing high levels of purified isoflavones, is less established.
Anti-cancer effects of isoflavones not related to estrogen activity
Isoflavones inactivate an array of enzymes involved in the cancer process such as tyrosine kinase and aromatase-5a-reductase. Enhanced activity of tyrosine kinases has been implicated with many cancers. In vitro tests have shown that genistein can inhibit the activity of tyrosine kinase. Genistein inhibits particularly the nutrition of the tumor, by reducing the formation of the blood vessels, thereby slowing down its growth. Finally, isoflavones are strong antioxidants, similar to vitamin C and E, and help to neutralize free radicals which play an important role in the mutagenesis and carcinogenesis.
 Andres et al. Crit Rev Toxicol. Risks and benefits of dietary isoflavones for cancer. 2011 Jul;41(6):463-506.