Hybrid zones formed between recently diverged populations offer an opportunity to study the mechanisms underlying reproductive isolation and the process of speciation. Here, we use a combination of analytical theory and explicit forward simulations to describe how selection against hybrid genotypes impacts patterns of introgression across genomic and geographic space. By describing how lineages move across the hybrid zone, in a model without coalescence, we add to modern understanding of how clines form and how parental haplotypes are broken up during introgression. Working with lineages makes it easy to see that clines form in about 1/s generations, where s is the strength of selection against hybrids, and linked clines persist over a genomic scale of 1/T, where T is the age, in generations, of the hybrid zone. Locally disadvantageous alleles tend to exist as small families, whose lineages trace back to the side from which they originated at speed s dispersal distances per generation. The lengths of continuous tracts of ancestry provide an additional source of information: blocks of ancestry surrounding incompatibilities can be substantially longer than the genomewide average block length at the same spatial location, an observation that might be used to identify candidate targets of selection.