Human genomic data carry unique information about an individual and offer unprecedented opportunities for healthcare. The clinical interpretations derived from large genomic datasets can greatly improve healthcare and pave the way for personalized medicine.Sharing genomic datasets, however, pose major challenges, as genomic data is different from traditional medical data, indirectly revealing information about descendants and relatives of the data owner and carrying valid information even after the owner passes away. Therefore, stringent data ownership and control measures are required when dealing with genomic data. In order to provide secure and accountable infrastructure, blockchain technologies offer a promising alternative to traditional distributed systems. Indeed, the research on blockchain-based infrastructures tailored to genomics is on the rise. However, there is a lack of a comprehensive literature review that summarizes the current state-of-the-art methods in the applications of blockchain in genomics. In this paper, we systematically look at the existing work both commercial and academic, and discuss the major opportunities and challenges. Our study is driven by five research questions that we aim to answer in our review. We also present our projections of future research directions which we hope the researchers interested in the area can benefit from.