Some of the most productive organisms on earth reproduce asexually much of the time. Much of evolutionary genomic inference relies on coalescence but almost all previous theory assumes full sex (or haploidy). I will discuss our recent work integrating partial asexuality into the coalescent framework to understand how low rates of sex affects coalescence, highlighting the importance of gene conversion. I will also how low rates of sex greatly enhance background selection, thereby reducing effective population size, via two separate effects. Finally, I will present some new population genomic data from a facultatively sexual plant, the duckweed Spirodela polyrhiza.