Advances in the genetic analysis of humans have revealed a surprising abundance of local relatedness between purportedly unrelated individuals. Where common mutations classically inform us of ancient relationships, such segments of pairwise identical by descent (IBD) sharing from a common ancestor are the observable traces of recent inter-mating. Combining these two distinct sources of information can help disentangle the complex genetic structure and flux in human populations. When considered together with a heritable trait, the segments can also be used to interrogate unascertained rare variation and help in locating trait-effecting loci. This work presents methods for comprehensive analysis of population-wide IBD and explores applications to disease and the understanding of recent genetic variation. We propose several strategies for efficient detection of IBD segments in population genotype data. Our novel seed-based algorithm, GERMLINE, can reduce the computational burden of finding pairwise segments from quadratic to nearly linear time in a general population. We demonstrate that this approach is several orders of magnitude faster than the available all-pairs methods while maintaining higher accuracy. Next, we extended the GERMLINE technique to process cohorts of unlimited size by adaptively adjusting the search mechanism to meet resource restrictions. We confirm its effectiveness with an analysis of 50,000 individuals where contemporary methods can only process a few thousand. One draw-back of these two algorithms is the dependence on phased haplotype data as input - a constraint that becomes more difficult with large populations. We propose a solution to this problem with an algorithm that analyzes genotype data directly by exploring all potential haplotypes and scoring each putative segment based on linkage-disequilibrium. This solution significantly outperforms available methods when applied to full sequence data and is computationally efficient enough to analyze thousands of sequenced genomes where current methods can only determine haplotypes for several hundred. Secondly, we outline two algorithms for analyzing available IBD segments to increase our understanding of rare variation and complex disease. Motivated by whole-genome sequencing, we present the INFOSTIP algorithm, which uses IBD segments to optimize the selection of individuals for complete population ascertainment. In simulations, we show that INFOSTIP selection can significantly increase variant inference accuracy over random sampling and posit inference of 60% of an isolated population from 1% optimally selected individuals. Seeking to move beyond pairwise IBD segment analysis, we describe the DASH algorithm, which groups shared segments into IBD "clusters" that are likely to be commonly co-inherited and uses them as proxies for un-typed variation. In simulated disease studies, we show this reference-free approach to be much more powerful for detecting rare causal variants than either traditional single-marker analysis or imputation from a general reference panel. Applying the DASH algorithm to disease traits from different populations, we identify multiple novel loci of association. Together, these novel techniques integrate the power of population and disease genetics.