Worldwide freezing and thawing of embryos has been increasingly used since the first infant was born as a result of this technique in 1984. The use of frozen embryo replacement (FER) currently even exceeds the number of fresh cycles performed in some countries. This article discusses the pros and cons of FER versus fresh-embryo transfer with regard to both single-cycle and cumulative pregnancy and delivery rates. The review discusses the obvious advantages of FER: minimizing the proportion of pharmacological and surgical treatments, and lowering the risk of ovarian hyperstimulation syndrome and multiple pregnancies, thereby increasing the safety for mother and child. Finally the article describes the accumulating literature on perinatal and long-term child outcome after transfer of frozen/thawed embryos, including a discussion on the concerns regarding cryo techniques and their possible roles in the subsequent development of fetus and child. Because larger and more detailed data sets are available for early cleavage-stage embryo freezing and slow freezing, they are the main focus of this review.