Telomeres are regions of repetitive nucleotide sequences capping the ends of eukaryotic chromosomes that protect against deterioration, and whose lengths can be correlated with age and adverse health risk factors. Yet, given their length and repetitive nature, telomeric regions are not easily reconstructed from short-read sequencing, thus making telomere sequencing, mapping, and variant resolution challenging problems. Recently, long-read sequencing, with read lengths measuring in hundreds of kilobase pairs, has made it possible to routinely read into telomeric regions and inspect their sequence structure. Here, we describe a framework for extracting telomeric reads from whole-genome single-molecule sequencing experiments, including de novo identification of telomere repeat motifs and repeat types, and also describe their sequence variation. We find that long, complex telomeric stretches and repeats can be accurately captured with long-read sequencing, observe extensive sequence heterogeneity of human telomeres, discover and localize noncanonical telomere sequence motifs (both previously reported, as well as novel), and validate them in short-read sequence data. These data reveal extensive intra- and inter-population diversity of repeats in telomeric haplotypes, reveal higher paternal inheritance of telomeric variants, and represent the first motif composition maps of multi-kilobase-pair human telomeric haplotypes across three distinct ancestries (Ashkenazi, Chinese, and Utah), which can aid in future studies of genetic variation, aging, and genome biology.