Resting state functional magnetic resonance imaging (rfMRI) can be used to measure functional connectivity and then identify brain networks and related brain disorders and diseases. To explore these complex networks, however, huge amounts of data are necessary. Recent advances in neuroimaging technologies, and the unique methodological approach of rfMRI, have enabled us to an era of Biomedical Big Data. The recent progress of big data sharing projects with their challenges are discussed. This increasing amount of neuroimaging data has greatly increased the importance of developing preprocessing pipelines and advanced analytic techniques, which are better at handling large-scale datasets. Before applying any analysis method on rfMRI data, several preprocessing steps need to be applied to reduce all unwanted effects. Three alternative ways to get access to big preprocessed rfMRI data are presented involving the minimal preprocessing pipelines. There are several commonly used methods to examine functional connectivity. However, they become limited in the analysis of big data, and a new tool to explore such data is necessary. We propose a number of novel methods rooted in algebraic topology and collectively referred to as Topological Data Analysis to rfMRI functional connectivity. Their properties for big data analysis are also discussed.