You can't tell by looking at your favorite edible mushroom (or just any mushroom if you hate mushrooms), but a fungus is actually a closer relative to you than it is to a plant.
How we know that? Fungi don't exactly have feet or eyes or heads or anything that we have.
That's because there's more to a mushroom than meets the eye. We're constantly changing the tree of life, changing our minds about who's related to what and when the species diverged from an ancestor. We regularly cut off tree branches and twigs and superglue them to an alternate location. Molecular biology, understanding cells on the teeniest tiniest level, comes a long way in helping us make those connections.
Historically, molecular biology has been used to figure out what species are related to each other through DNA sequencing, as well as verify a baby's daddy.
rRNA sequencing has also been a popular tool used to cut up and reconfigure the tree of life in prokaryotes. rRNA is the type of RNA that makes up ribosomes, the little machinery that performs translation. All cells have ribosomes—both prokaryotic and eukaryotic. But the rRNA that makes up these ribosomes is different. Prokaryotes contain a small rRNA known as 16s rRNA, and it's been sequenced in bacteria like crazy. By sequencing these rRNAs, we can look at how similar they are between organisms on a genetic level.
Currently, scientists are starting to sequence the eukaryotic version of this rRNA (called 18s rRNA due to its larger size). While these sequencing methods haven't exactly shaken many tree branches yet, it has a lot of potential as a method that could tell us a lot more about the differences and similarities between different organisms. We know that fungi are more like us than plants, because we do things like make our own food and don't do things like photosynthesize. Additionally, fungi and some animals share the molecule chitin, which no plant contains. These are good lines of evidence, but not totally fool-proof. Sequencing our rRNA could be the icing-like proof on this cake and solidify the similarities between you and the World's 10 Most Amazing Mushrooms.