Once an abstract branch of mathematics, topology now finds its applications in many scientific fields. Algebraic topology provides tools resilient to noise and effective in analyzing complicated data sets; persistent homology is one of such emerging tools from algebraic topology; it has been proved successful in analyzing data sets which traditional methods cannot cope with well.

In the first part of the talk, I will give a quick review on persistent homology and basic invariants of filtered space drawn from persistent homology. Some recent applications of persistent homology in sensor network and neuroscience are discussed in the second part.