ESP8266 power supply issues

[james_s]

Those are some seriously sharp spikes, I wonder what the IC is actually doing that's resulting in that? It almost looks like the result of shoot-through with a transistor bridge. Seems any board for one of these things should have a load of ceramic decoupling caps.

[LukeW]

Maybe it would help if you show us a schematic of what you've actually built?

And a photo too? (I suspect you've got issues that can't be seen just at the schematic level, such as large loops, dodgy connections, parasitic inductance, high-ESR bulk capacitors etc.)