The first documentated muddler minnow pattern goes back to 1926 in US. Even though nowadays muddler might sound synonimous of cone-head shaped deer hair fly, apparently the models in the early years did not have a thick bulky head but more sparse trimmed hair. This unweighted version is fished on floating lines as well as on sinking lines, imitating primarily a fish (gobius) but in the smaller hook sizes a big sedge or stonefly. Here below the original dressing:
hook extra long size 1 - 12, tail: mottled turkey, body: flat golden tinsel, underwing: sparse gray squirrel, wings: mottled turkey, head and hackle: natural deer hair

The adoption of the metal conehead helps fish this fly deep sunken. Leveraging on the heavy metail head, the fly enters the action scene at certain depth almost immediately. In trout areas characterized by strong currents and deep, realtively small pools, the imitation has to reach the depth fast, before being dragged away.
Thiy fly is a good imitation for the sculpin
Hook 1/0 - 2 extra long
Tail: mottled turkey
Body: flat golden tinsel
Wing: abundant tuft of brown fur reaching the start of the tail
Collar: deer hair
Head: metal conehead and trimmed deer hair

Many are the hypothesis for the success of the muddlers. The trimmed deer hair is able to capture some air, that once in water get released in the form of tiny gas bubbles, creating a living effect. Under the water the shaped bulky head generate water turbulences and vibrations like the ones generated by a real fish. The colour of the mottled turkey is close to forage fish presenet in most waters.
Additionally, other materials may be considered for the wings that may offer some translucence, like in a matuka style muddler.

Left:                                                                                                               Right:
For slower currents the movement of the rabbit fur                                         A moment of creativity at a tier's desk: the production
is fantastic in the role of a swimming creature.                                                lines up on the drying cat-walk..
Fur combined with the cone shape head key on visive                                   It is remarkable how some patterns seem to
and lateral line perception of fish.                                                                   be more prolific in fly boxes, following a sort of
                                                                                                                       of Lamarckian evolution.
                                                                   

A fat 3-pound brown trout caught in the Hyporhithron at sunset. I was swinging a dark fur muddler across a current when the big fish darted from an invisible hide at the bottom and snagged the fly.
Hook : up-eye salmon hook 1 - 8
Thread: black
Body: flat silver tinsel
Wing: black fur strip. 3-4 extra thin synthetic flashy fibers
Collar: mix of black, dark olive and natural deer hair, trimmed short in proximity of the conehead
Head: metal conehead.

In the lower part of the streams (Potamal), the fur muddler covers a wide spectrum of possible preys. Chub can grow up to 60 or more cm. and they like quite sized streamers. The soft fur gives its best in this type of waters.
In the picture on the right, at dusk a big chub could not resist a 8 cm. long fur muddler. Chub prefer a slow retrieve of the fly, with short strips.
This colour combination is one of my favourite:
Hook: 2 - 8 extra long
Thread: cream
Wing: barred grey/brown fur strip
Body: flat sliver tinsel
Collar: natural deer hair
Head: conehead

In largest sizes, muddler heads are accountable for pike, perch-pike, black bass and even salmon.
Its success is not only limited to rivers and lakes but extends to saltwater.
In the picture: the larger muddler for pikes are best fished with sinking lines.