Although breastfeeding is associated with many health-related benefits for both mothers and children, the WHO recommendation for exclusive breastfeeding is not achieved by the majority in any WHO region. This paper aims to present the current state of research on challenges and choices in breastfeeding healthy, sick and preterm babies. The research was organized as a systematic search in PubMed and the study was performed as a narrative review after applying the PRISMA protocol. Finally, n = 57 studies were included. Both barriers and support factors emerge as a complex interaction of individual, group and societal factors, the precise understanding of which is relevant to increasing breastfeeding rates in the future. Knowledge as well as practical skills proved to be generally helpful, whereas the lack of breastfeeding support for mothers, who are often separated from their premature babies in hospital, was identified as a key risk factor for this subgroup. Appropriate training for healthcare professionals can improve the situation as a result. After discharge, workplace-related barriers are of major concern to allow further breastfeeding when maternity leave ends. Thus, the promotion of breastfeeding must be perceived as a task for society as a whole.