At the beginning of the twenty-first century, intergenerational relations remain a key aspect of the future development and sustainability of the European social model. In the present paper, patterns of intergenerational support and the main driving factors behind individuals' transfer behavior are explored. In particular, the data form the Survey of Health, Ageing, and Retirement in Europe are utilized to shed light on the main factors behind the likelihood and intensity of social support, and financial help provided to and received from other family members by ageing and elderly Europeans. The analysis also takes into consideration patterns and factors correlated with grandparenting activities. Finally, special attention is devoted to the condition of those individuals who are sandwiched between care obligations toward their elderly parents and young adult children. It is shown that the likelihood of the exchange of support between family generations is highest in Scandinavian countries and lowest in Southern Europe. The intensity of support follows an opposite North-South gradient. In addition, relevant gender-related inequalities are documented. In general, time-demanding support obligations are more likely to fall on the shoulders of women in the early stage of their later life, while mainly benefitting elderly men.