Hybrid zones, where genetically distinct groups of organisms meet and interbreed, offer valuable insights into the nature of species and speciation. Here, we present a new R package, bgchm, for population genomic analyses of hybrid zones. This R package extends and updates the existing bgc software and combines Bayesian analyses of hierarchical genomic clines with Bayesian methods for estimating hybrid indexes, interpopulation ancestry proportions, and geographic clines. Compared to existing software, bgchm offers enhanced efficiency through Hamiltonian Monte Carlo sampling and the ability to work with genotype likelihoods combined with a hierarchical Bayesian approach, enabling inference for diverse types of genetic data sets. The package also facilitates the quantification of introgression patterns across genomes, which is crucial for understanding reproductive isolation and speciation genetics. We first describe the models underlying bgchm and then provide an overview of the R package and illustrate its use through the analysis of simulated and empirical data sets. We show that bgchm generates accurate estimates of model parameters under a variety of conditions, especially when the genetic loci analyzed are highly ancestry informative. This includes relatively robust estimates of genome‐wide variability in clines, which has not been the focus of previous models and methods. We also illustrate how both selection and genetic drift contribute to variability in introgression among loci and how additional information can be used to help distinguish these contributions. We conclude by describing the promises and limitations of bgchm, comparing bgchm to other software for genomic cline analyses, and identifying areas for fruitful future development.