Beginning with the Johnson Lindenstrauss lemma as motivation, we will look at oblivious subspace embeddings (OSEs) as a tool for dimension reduction in randomized numerical linear algebra. We will then discuss current work about showing the existence of sparse OSEs with optimal parameters. However, the main focus of this talk will be on understanding basic Gaussian examples and applications. The aforementioned current work is joint work with Michal Derezinski, Xiaoyu Dong and Mark Rudelson.