Ilsdorf had formerly been a part of the Province of Upper Hesse in the Landgraviate of Hesse-Darmstadt, while Solms-Ilsdorf was ruled by the Counts of Solms.

The name Mücke was mentioned in connection with this region in a Merlau parish taxation roll in 1482.

The Jugendparlament has the right to speak and make motions on the municipal council's youth, sport and cultural committee.

The community of Mücke maintains a partnership with: The community of Mücke has at its disposal, through the Homberg (Ohm) Autobahn interchange (A5) and Federal Highway (Bundesstraße) 49 that runs through the municipal area, very good transport connections.

A few years ago, at the Autobahn interchange, the "Am Gottesrain" industrial park was established complete with an off-Autobahn service centre ("Autohof").

On the Kratzberg in the Nieder-Ohmen rural area, the Luftsportgruppe Mücke e. V. runs a model glider airfield.