Local ancestry is central to a variety of inference problems in population and medical genetics. Here I propose new methods for studying admixture demography and inferring non-crossover gene-conversion from admixture tracts. First, I present PAPI (Parental Admixture Proportion Inference), a Bayesian tool for inferring admixture proportions and admixture times from the un-genotyped parents of an admixed sample. PAPI's components are a binomial model of ancestry and a hidden Markov model (HMM) that relies on a pooled-Markovian approximation to pedigree crossover dynamics, recapitulates admixture tract length distributions well, and serves as an important re-parameterization of transition probabilities. I show that PAPI outperforms existing tools and is highly accurate in simulated data as well as in ASW (African Ancestry in Southwest USA) trios. I apply PAPI to the PAGE dataset of African Americans and discover strong patterns of assortative mating by ancestry proportion: couples' ancestry proportions are highly correlated ($R=0.87$). Next I introduce a pedigree-based gene-conversion simulator and present an unbiased coalescent estimator for gene-conversion rates based on an algorithm for matching admixture tracts to a reference panel. Uniquely, this approach can also estimate local gene conversion rate estimates by leveraging more information than conventional methods. I will further demonstrate the effectiveness of a method that exploits the characteristic disruption of linkage disequilibrium (LD) patterns near gene-conversion sites to classify the polarity of gene-conversions - i.e whether a converted tract is on an admixed haplotype or a reference haplotype. Finally, I present results from an empirical study into the impact of phasing on local ancestry infrence (LAI). These results can guide study design decisions and choice of phasing and LAI tools downstream across many settings. Importantly, I find that phase-agnostic LAI outperforms phase-sensitive LAI, and that care must be taken when deciding to phase data if highly accurate LAI is desired.