Is there a way to increase the spacing between the legend labels in the histogram below so that they are legible? Thanks!
using LaTeXStrings
y1 = rand(100)
y2 = rand(100)
histogram(y1, ylims = (0,50), label = L"\left\Vert\beta_{1}^{2}-\beta_{2}^{2}\right\Vert")
histogram!(y2, label = L"\left\Vert\beta_{2}^{2}-\beta_{3}^{2}\right\Vert")
If you use the plotly() backend: latex - Julia plotting issues: label overlap and LaTeXStings expansion - Stack Overflow
I didn’t find a way to do it with the gr() backend. You can control the font with, say, legendfontsize=14.0 and there is an option for labelspacing=0.1 (typical values seem to be small), but I’m not sure what labelspacing actually does: it sounds like it might control the horizontal spacing, but I did not notice an effect on your plot. Hopefully someone from Plots.jl can help you with this. Alternatively, introducing a line skip inside the LaTeX string: I also failed to achieve that with the usual suspects: "\\n", "\\\", "\\vspace{2em}" 
@Dan.phi, with Plots.jl you often need to be creative and it will rarely disappoint.
using LaTeXStrings, Plots; gr()
y1, y2 = rand(100), rand(100)
histogram(y1, ylims = (0,50), label = L"\left\Vert\beta_{1}^{2}-\beta_{2}^{2}\right\Vert")
scatter!([minimum(y1)],[0], label=" ", ms=0, mc=:white, msc=:white)
histogram!(y2, label = L"\left\Vert\beta_{2}^{2}-\beta_{3}^{2}\right\Vert", legendfontsize=10)
NB: nevertheless, your code produces a legend that is perfectly legible in Julia 1.6.1, Win 10, Plots v1.16.3, gr backend
you added an invisible legend item with scatter! in order not to interfere with the other two histogram calls, right? Clever. 
This sort of trick is often needed.
I opened an issue because I think it should not be too hard to add a padding option. There is such an option for the plot area itself and the legend is constructed in an analogous way. Unfortunately I don’t know enough about Plots to create a PR, but hopefully it’s a reasonable request.
Huge thanks to @t-bltg, who in response to the issue mentioned above, put together a PR that allows more vertical space inside legends, fixing the OP and allowing more flexibility in general. 
Happy to help 
