The revolution in next-generation DNA sequencing technologies is leading to explosive data growth in genomics, posing a significant challenge to the computing infrastructure and software algorithms for genomics analysis. Various big data technologies have been explored to scale up/out current bioinformatics solutions to mine the big genomics data. In this review, we survey some of these exciting developments in the applications of parallel distributed computing and special hardware to genomics. We comment on the pros and cons of each strategy in the context of ease of development, robustness, scalability, and efficiency. Although this review is written for an audience from the genomics and bioinformatics fields, it may also be informative for the audience of computer science with interests in genomics applications.