To date, fewer than a dozen studies of grandparenting have been reported. While a serious reading of the available data is premature, several lines of inquiry and issues can be identified and discussed. This presentation explores six general topics: (1) age and cohort differences, (2) sex differences, (3) social group differences, (4) individual variations in style, (5) relation to the family as a system, and (6) reciprocal influence of grandparents and grandchildren. Self reports indicate age differences in feelings of closeness between grandchildren and grandparents. Male grandparents may attempt to influence their grandchildren more than do grandmothers, but grandmothers are more likely to have warm relationships with their grandchildren than are grandfathers. Relations with grandchildren appear to be more alike than different across ethnic and class groups. Different styles of grandparenting have been found to be characteristic of particular cultures, life stages, and personalities. Additional family studies which view the family as a system extending over several generations and focus on intra-family structures and functions are recommdended. Research indicates that grandparents and adult grandchildren acknowledge reciprocal attempts to influence each other -- on certain topics. (Author/RH)