Like mushrooms, moles tend to surface during the spring and fall, when the soil is cool and moist. Driven into their deeper tunnels during the heat of summer and the frigid months of winter, they follow their prey (earthworms, grubs, insects) into the upper layers of the soil when milder conditions prevail. It is then, of course, that they endure the wrath of lawn masters, who attack them with a variety of chemicals and traps.
Rather solitary for much of their lives, moles mate in late winter and a litter of 2-6 young are born in a deep nest chamber by mid spring; each will be on its own within a month, equipped to dig tunnels at a phenomenal rate (up to 18 feet per hour for adult moles). While their deeper channels are extensive and permanent, those close to the surface (that draw our attention and ire) provide access to temporary foraging areas. Though we might mine these areas with a variety of poisons and contraptions, they can easily move off to greener pastures and any success that we might have is always temporary.
As naturalists know, moles play an important role in soil aeration and insect control and their "unsightly" excavations are the sign of a healthy ecosystem. Mammalian insectivores (related to shrews and bats), moles often consume their body weight in prey through the course of a day and may ingest 50 pounds of invertebrates over a year; it is best that we leave the control of their population to snakes, skunks, raccoons, weasels, fox, coyotes and owls. Better yet, reduce their natural habitat by widening your shrub borders and minimizing your lawn space; that will send the moles off to your neighbor's manicured carpet.