I know of two options to put figures in landscape.
The first is to use the
sidewaysfigure environment. This works very well when it comes to keeping the sequence of figures. However, it leaves the page in portrait and turns the figure instead which makes it hard to read online. I also could not figure out how to put several figures (not sub-figures) on one page.
The second is to use a combination of the
landscape environment and
\afterpage. This works very well when it comes to showing pages in landscape with the figures easily readable. However, this messes up the sequence of floats. (See sidewaysfigure and landscape and, for the numbering problem, How to get landscape float with correct numbering?.)
Is there a proper way to get the best of both worlds, i.e. landscape pages while keeping the order of figures?
Note on the chosen solution
There are a couple of limitations with the chosen answer. On how to fix them see How to avoid additional page getting rotated?.