The human brain can be conceptualized as a dynamic system of coordinated functional sources, governed by the fundamental principles of functional segregation and integration. These functional sources — intrinsic connectivity networks (ICNs) — are characterized by temporally synchronized neural activity and can be assessed non-invasively using resting state functional magnetic resonance imaging (rs-fMRI) with independent component analysis (ICA). However, The ICNs derived from traditional ICA approaches are subject to three fundamental limitations: they reflect only a single spatial scale, obscuring the hierarchical and multi-scale organization of brain functional sources; they lack the granularity necessary to capture fine-grained functional sources and their meaningful connectivity patterns; and they are estimated from the full cohort as a single homogeneous group, rendering them blind to neurobiological heterogeneity. The present dissertation addresses these limitations through three complementary methodological contributions. The first contribution, Telescopic ICA (T-ICA), introduces a novel recursive framework that constructs spatial functional hierarchies by leveraging ICNs estimated at a larger scale to guide decomposition at finer scales, revealing how large-scale ICNs decompose into granular ICNs and identifying significant diagnostic group differences in schizophrenia that are missed by single-scale approaches. The second contribution applies very high model order ICA to over 100,000 subjects, yielding NeuroMark-500 — a comprehensive and replicable atlas of granular ICNs and demonstrates its clinical value by characterizing functional network connectivity alterations in schizophrenia and their associations with cognitive performance. The third contribution introduces Concurrent Supervised-Unsupervised ICA (CSU-ICA), a novel framework that jointly optimizes supervised sex labels and unsupervised biotype assignments within a single iterative ICA procedure. Preliminary validation demonstrates biotype recovery on synthetic data and identifies statistically significant sex-specific biotypes across the psychosis spectrum, providing early evidence that sex-informed ICA can reveal neurobiological heterogeneity inaccessible to conventional approaches. Together, T-ICA, NeuroMark-500, and CSU-ICA represent complementary methodological advances that expand the analytical toolkit for rs-fMRI research — capturing ICNs across multiple scales, with fine-grained functional granularity, and with sensitivity to sex specific neurobiological structure — with broad potential to enhance the clinical utility of rs-fMRI and accelerate the investigation of psychiatric and neurological disorders.