Diverse disciplines, including Human-Computer Interaction have explored how health technologies can support families in dealing with health conditions and in promoting healthy living. With the changing of family structures and the increase of variety in family backgrounds, however, there is still a need to understand the extent which existing studies have addressed family health needs by proposing technological solutions. In this paper, we present a systematic review of the literature in order to see which family health topics have been researched extensively or not, and to identify hidden aspects and opportunities for family-centered health technology research. We had a final sample of 55 papers from diverse sources in this process. Our findings highlight characteristics of the studies, families, and health design. We also describe existing technological solutions and evaluation measures. Based on our findings, we discuss factors that were comprehensively studied and others that need further exploration in future research related to family-centered health technology.