Recent years, genomics and big data analytics have been widely applied and have significant impacts in various important areas of social life worldwide. The development of the next-generation sequencing (NGS) technologies, such as whole-genome sequencing (WGS), whole-exome sequencing (WES), transcriptome, and/or targeted sequencing, has enabled quickly generating the genomes of interested living organisms. Around the world many nations have invested in and promoted the development of genomics and big data analytics. A number of well-established projects on sequencing of human, animal, plant, and microorganism genomes to generate vast amounts of genomic data have been conducted independently or as collaborative efforts by national or international research networks of scientists specializing in different technical fields of genomics, bioinformatics, computational and statistical biology, automation, artificial intelligence, etc. Complicated and large genomic datasets have been effectively established, storage, managed, and used. Vietnam supports this new field of study through setting up governmental authorized institutions and conducting genomic research projects of human and other endemic organisms. In this paper, the research, development, and applications of genomic big data are reviewed with focusing on: (i) Available sequencing technologies for generating genomic datasets; (ii) Genomics and big data initiatives worldwide; (iii) Genomics and big data analytics in selected countries and Vietnam; (iv) Genomic data applications in key areas including medicine for human health care, agriculture - forestry, food safety, and environment.