Research in genetics and genomics is advancing at a fast pace, and thus keeping up with the most recent findings and conclusions can be very challenging. At the same time these recent findings and conclusions have made necessary a reconceptualization of genes and heredity, both in science and in science education, beyond the mostly gene-centred view of the twentieth century. The teaching of genetics at schools should have a key role in helping students achieve genetics literacy. However, the literature on research in genetics education reports persistent difficulties and misunderstandings. We first consider the public understanding of and the attitudes towards genetics. Then, we review the most recent literature and present the most typical conceptions found among secondary students in various countries, ages and backgrounds. We argue that particular factors such as intuitive thinking, teachers, textbooks, and the media affect students' development of erroneous or outdated ideas related to genetics. Finally, we suggest how these problems might be addressed in order for genetics teaching at the secondary level to fulfil the aim of contributing to students' genetics literacy in the current post-genomic era.