Solid tumours need a blood supply, and a large body of evidence has previously suggested that they can grow only if they induce the development of new blood vessels, a process known as tumour angiogenesis. On the basis of this hypothesis, it was proposed that anti-angiogenic drugs should be able to suppress the growth of all solid tumours. However, clinical experience with anti-angiogenic agents has shown that this is not always the case. Reports of tumours growing without the formation of new vessels can be found in the literature dating back to the 1800s, yet no formal recognition, description and demonstration of their special biological status was made until recently. In 1996, we formally recognized and described non-angiogenic tumours in lungs where the only blood vessels present were those originating from normal lung tissue. This is far from an isolated scenario, as non-angiogenic tumour growth has now been observed in tumours of many different organs in both humans and preclinical animal models. In this Opinion article, we summarize how these tumours were discovered and discuss what we know so far about their biology and the potential implications of this knowledge for cancer treatment.