Finland provides unique opportunities to investigate both population and medical genomics because of its adoption of unprecedented uniformity in national electronic health records, concerted coordination of research centers across the country, detailed historical records, as well as recent population bottlenecks that drove specific disease alleles to high frequency. We investigate recent population history (up to ~50 generations ago), particularly relevant to rare, disease-conferring alleles, using identity-by-descent (IBD) haplotype sharing in >10,000 Finns. We compare IBD sharing in Finland to nearby Scandinavian countries with considerably different population histories, including >8,000 Swedes and >30,000 Danes. We find drastically more sharing on average in Finns, including many long tracts. By leveraging fine-scale birth record data, we find a non-linear decay of pairwise IBD sharing with increasing distance across Finland. This arises from pockets of excess IBD sharing; e.g. pairs of individuals from northeast Finland share on average several-fold more of their genome IBD than pairs from southwest regions containing the major cities of Turku and Helsinki. We demonstrate inference of recent migration patterns from IBD sharing patterns. For example, high IBD sharing in northeast Finland radiates from north to south rather than to the west, indicating a coastal wave of migration. We also investigate recent effective population size changes across regions of Finland and find evidence supporting the distinction between early and late settlement areas. However, our results indicate a more continuous flow of migration than previously posited, with a minimum Ne occurring ~12 generations ago in the northernmost Lapland region and moving further back in time to the south, with a bottleneck detectable in the early settlement area ~40 generations ago. Lastly, we leverage IBD sharing for genetic disease mapping and show that rare, functional haplotypes show more significant association via IBD mapping than single variants with linear mixed effect models.