Tail wagging is a conspicuous behaviour in domestic dogs (Canis familiaris). Despite how much meaning humans attribute to this display, its quantitative description and evolutionary history are rarely studied.

Source : Biology Letters, Jan. 2024

It's currently not clear why dogs wag their tails so much (when compared to other canids such as wolves etc.). It seems probable that the wagging serves some kind(s) of communication function, but exact details are currently lacking.

Despite the ubiquity of dogs in our lives and all the meaning we ascribe to tail wagging, quantitative studies to date have led to patchy results and a structured theoretical framework is missing."

[ source as above ]

The study suggests that the (possibly exaggerated) wagging could be a by-product of human-led breeding programmes. Either because the dogs have become 'imfantilised' (compared to their wild cousins), or, that human breeders have selected for dogs which, from a human point of view, seem to be 'happier'.

There is some evidence that the tail wagging can be asymmetric (i.e. with a left or right bias) according to the circumstances, but again, details are far from clear.

We consider whether such asymmetry in motion of the tail, a crucial appendage in intra-specific communication in all canids, provides visual information to a conspecific leading to differential behaviour.”

See : Behavioural responses of dogs to asymmetrical tail wagging of a robotic dog replica ^{[ paywalled ]} Asymmetries of Brain, Behaviour, and Cognition, Volume 16, 2011 - Issue 2