Scientific American is reporting on the research of behavioural ecologist Daniela Rößler into the sleep behaviours of jumping spiders.

After first observing that these spiders would occasionally hang motionless (and presumably asleep) on the ends of their silk threads, Rößler noticed something interesting.
From time to time they would display a distinct twitching.

Hmmm, she thought, that kinda looks like the behaviours when dogs or cats are dreaming.
Could it be that spider’s dream?

She then studied the ‘sleeping’ movements of 34 spiderlings that have translucent exoskeletons. As well as the familiar dream twitchings, you can also see movements in the tubes that control their retinas (which as a mild arachnophobic I find somewhat disturbing).

The theory is that this could possibly be REM sleep related to visual dream sequences.

Dreaming offers an entry point into questions of awareness in other animals: it is difficult to imagine that even a simple dream is possible without something like an ego or an “I” experiencing it, he adds. So if spiders dream, “it might mean that we start talking about spiders having something like a minimal self,” says Peña-Guzmán, who was not involved with the spider research.

https://www.scientificamerican.com/article/spiders-seem-to-have-rem-like-sleep-and-may-even-dream1/

You can read the full article here.