In recent decades, major theoretical and technological advances have been achieved in the field of immunology. These have allowed the scientific community to analyse the immune system in a much more sophisticated manner than was possible even 20 years ago. Moreover, great theoretical changes have also occurred in gerontology - in particular, the hypothesis has been put forward that ageing and diseases are two different phenomena, and that successful ageing, i.e. ageing in good psychophysical conditions, is really possible for most humans and animals. Immunosenescence was then carefully investigated, either in selected healthy people of advanced age or in the oldest old people, such as healthy centenarians. The main results showed that most immune parameters are indeed well preserved even at this far advanced age. This paper deals with some of the most important theoretical problems of immunosenescence. An immunological tenet was that the most important phenomenon of immunosenescence is the involution of the thymus. In most textbooks and papers it is taken for granted that the thymus starts its involution immediately after puberty. When people aged 60-65 were considered old, it was not difficult to think that they could live for the rest of their life with a fully involuted thymus. The findings on centenarians challenge this tenet, as they have only a small reduction of T lymphocytes, and a relatively normal number of virgin and memory T cells, together with a functional T cell repertoire. Other observations reported here on centenarians, concerning the activity of B lymphocytes and the cytokine network, as well as those on the well-preserved innate immunity and the cells' capability of undergoing proliferation after appropriate stimuli, suggest that complex immune changes occur with age, but also indicate that we have to modify our attitude, to grasp the new scenario which is emerging. Immunosenescence can no longer be considered as a unidirectional deterioration, and this complex phenomenon is much better described by terms such as 'remodelling', 'reshaping' or 'retuning'