Cirroteuthis muelleri, also known as the big-finned jellyhead,[2] was the first cirrate octopus species (and genus) to be scientifically described (in 1836).

[6] Statements that C. muelleri reaches up to 1.5 m total length are erroneous (and involve unidentified Cirrothauma, then regarded as Cirroteuthis sp.,[7] being mistakenly assumed to be C.

These are elongate, fleshy tendrils set along the sides of the oral surface of the arms, the longest being in the mid-arm region.

[5][9] Cirroteuthis muelleri is benthopelagic, meaning it is found swimming or drifting in the 10 m (33 ft) or so immediately above the sea bed.

[8] At these depths, practically no light penetrates, the temperature is about 4 °C, and observation is only possible by submersible, which makes these octopuses difficult to collect.

In a study of Arctic cephalopods, three specimens of Cirroteuthis muelleri, all female, were caught near the ocean floor at 3,000–3,300 m (9,800–10,800 ft).