Cancer remains a leading cause of death in the USA and around the world. Although the current synthetic inhibitors used in targeted therapies have improved patient prognosis, toxicity and development of resistance to these agents remain a challenge. Plant-derived natural products and their derivatives have historically been used to treat various diseases, including cancer. Several leading chemotherapeutic agents are directly or indirectly based on botanical natural products. Beyond these important drugs, however, a number of crude herbal or botanical preparations have also shown promising utility for cancer and other disorders. One such natural resource is derived from certain plants of the family Annonaceae, which are widely distributed in tropical and subtropical regions. Among the best known of these is Annona muricata, also known as soursop, graviola or guanabana. Extracts from the fruit, bark, seeds, roots and leaves of graviola, along with several other Annonaceous species, have been extensively investigated for anticancer, anti-inflammatory and antioxidant properties. Phytochemical studies have identified the acetogenins, a class of bioactive polyketide-derived constituents, from the extracts of Annonaceous species, and dozens of these compounds are present in different parts of graviola. This review summarizes current literature on the therapeutic potential and molecular mechanism of these constituents from A.muricata against cancer and many non-malignant diseases. Based on available data, there is good evidence that these long-used plants could have both chemopreventive and therapeutic potential. Appropriate attention to safety studies will be important to assess their effectiveness on various diseases caused or promoted by inflammation.