Playlists on iPhone (workaround to save it to laptop, or at least to a new phone)

I know that itunes inexplicably no longer allows you to see your iphone playlists. This is a huge problem when I realize I've spent the last year or two building out playlists on my phone, but when I get a new phone the work will be wasted. Other than manually building it within itunes one song at a time (in which case might as well not even get an iphone next time), is there a workaround to download the playlists so I can import them into my next phone? Also so I can use the playlists on my computer? (I'm not trying to get the songs off of my phone, just the organized playlists).

Alternatively can someone at an Apple store help me transfer the playlists to a new phone? When I got my current phone and restored from backup the playlists were not included so I'm worried I can't get a new phone without giving up the playlists or manually (and frustratingly) rebuilding them. Thanks for any help!