During the 1930's and 1940's there were criminals thought to be "untouchable", mainly due to immunity from the the law which itself was crooked. Our crooks today used a different technique to try accomplishing the same ends.
However, on Earth-Two a gang known as the Invisible Band (Bad Beau, Prexy, Doodler, Carat, and One-Hair) pulled off their schemes without being seen. Similarly, three crooks on Earth-One known as the Intangibles went the phantom route using advanced technology to phase through objects. However, Superman, Elongated Man, Robin and later Looker defeated the trio in their two appearances, the second when they were rechristened the Untouchables. Similarly, the Invisible Band was defeated by the Justice Society of America with the aid of their cleaning woman's nephew, an amateur detective who tracked them down.