Heaviside, a Londoner, was a nephew of Charles Wheatstone. Being very deaf, he was hampered in school, and was largely self-taught. He was interested in the transmission of electrical signals and used Maxwell's equations to develop a practical theory of cable telegraphy, introducing the concepts of self inductance, impedance, and conductance. However, his early results were not recognized, possibly because the papers were written using his own notation.

After radio waves had been transmitted across the Atlantic in 1901, he suggested (1902) the existence of a charged atmospheric layer that reflected the waves. The same year Arthur Kennelly independently suggested the same explanation. The Heaviside layer (which is sometimes called the Kennelly–Heaviside layer) was detected experimentally in 1924 by Edward Appleton.

Later in life his fame grew and he was awarded an honorary doctorate at Göttingen and was elected a fellow of the Royal Society in 1891.