They are of a family of birds which include the wild Wood Pigeons, and various types of Doves.

The city Pigeons are very messy and are classed as vermin ('rats with wings' some call them). They are multi partner and the males spend most of their time trying to mate. They can be invasive and destructive in their ways.
I prefer the Wood Pigeons which are fatter and smarter in appearance, and while not solitary seem to have different habits. They are very destructive to gardens and will wipe out peoples cabbages and peas.
Of course pigeons are selected for their ability to find direction and carry messages and have been doing so for at least hundreds of years.

Then there's Doves, which are very loyal partners and make the familiar 'cooing' sound. They like seeds are not destructive to cabbages (at least not mine!). They are more timid than Pigeons and I guess are a symbol of peace partly because of their peaceful and loving nature.

What 'Pigeon medicine' can others bring?