Question: pretty sure I saw a serial → wifi project using an ESP on this G+ community. Can’t find it now. Is there such a thing, or am I imagining it?
For little effort, the truly awesome ESPEasy project has that as one of its many features… It may be a bit overkill, and I haven’t personally used the serial option, but the rest have been faultless.
Esp-link
sorry, but I’m not seeing PPP/SLIP on either of those projects
you asked for serial-wifi and that’s what esp-link does. PPP/SLIP is a protocol while I thought you were after a convertor.
Petr, You beat me to it! 
Yep, I think you need to explain what you are trying to achieve. That ESP-link looks nice tho, I’ll remember that for next time!
esp-link is great. You don’t even need PPP/SLIP for TCP/IP on Arduino as you can use high-level things like HTTP GET/POST or even MQTT.
Sorry, I should have been clearer: this is specifically for PPP/SLIP on old computers with serial ports. I saw something about someone having developed this using an ESP board, and I thought I saw it written up here.
Nah, running a ppp server on chip is a bit beyond the scope of the esp itself. http://www.vcfed.org/forum/showthread.php?55527-Connecting-a-vintage-PC-to-the-internet-via-serial-port-and-wifi
Those guys did it using the same setup as we described, but pointing to a linux server running pppd to act as the (wifi) serial -> network bridge.
Still not that one; I know about the VCFED discussion