For starters, appreciate them. Unless they are creating a public hazard, there is a lot to admire about these animals.
This is a species that is making a comeback in North America. The soft undercoat of the beaver was used to make hats and after the decline of the Eurasian beaver, European hat manufacturers turned to North America, trapping them through the 1800s and decimating the population here.
Beavers are known for their ability to construct dams and lodges and can craft some impressive structures. Felling trees and cutting other vegetation with their sharpened teeth, hauling mud and stones to dam and lodge sites and occasionally re-purposing things like old tires and other trash, they build strong and stable dwellings and dams.
While their construction can be a nuisance if roadways are flooded or septic systems encroached upon, it is illegal in Massachusetts to disturb beaver dams or lodges without permits. A property owner may get an emergency permit through the Board of Health to trap the beavers. The breaching of a dam requires an emergency permit and approval from the Conservation Commission.
Removing a population of beavers is generally a temporary fix. Other beavers will quickly repopulate an area. One solution is to see if a water flow device or a pond leveler is a viable alternative to removal of the animals. This keeps the water level manageable while allowing the beavers to remain in an area.
If, however, there is no threat to human health and safety, the beavers are more likely than not performing a service to enhance our natural resources. The impoundments created by the dams, help with flood and fire control and provide a water resource during droughts by recharging groundwater. The expansion of wetlands is an excellent protector of water quality and enhances habitat for diverse species such as turtles, fish, otters, wood ducks and great blue herons.
Assuming that there isn't a threat to human health, it makes sense to let these animals coexist with us, allowing them to restore their habitat, while increasing the natural value of ours.