I just tried to do an emerge --update --world, and it failed
because

sys-apps/pam-login (is blocking sys-apps/shadow-4.0.15-r2)

I googled for that message, and the advice is "remove the
blocking package".

I removed pam-login, but that meant my system didn't have a
/bin/login anymore. Last I checked that was sort of vital, so
I re-emerged pam-login.

How do you figure out what to do in situations like this?

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Grant Edwards grante Yow! Did I say I was a
at sardine? Or a bus???
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