Poulsen, a Danish engineer, created and patented a machine that recorded onto magnetic tape. His called the invention a Telegraphone. There was no amplification and the recording quality was poor.
In 1928, Pfleumer, a German, vastly improved the magnetic tape. He named his device a Magnetophone. During WWII the Germans used it for communications and to spoof radio communications. Nazis time-shifted recorded conversations leaving allies unsure whether they were hearing intercepted real communications or purposefully misleading recordings.
American John Herbert Off captured the Magnetophone and, after the war, brought it to the US for commercialization. He teamed up with Russian immigrant Alexander M. Poniatoff who eventually created Ampex (Alexander M. Poniatoff Excellence) from the shell of a former company, Dalmo-Victor.
Existing recording technologies were not adequate for live broadcasts. But Ampex equipment offered vastly higher quality for live broadcasts. Therefore, radio broadcasts were virtually always live. Then superstar Bing Crosby heard the new technology and eventually decided to use Ampex equipment for his radio show. This enabled re-takes and post-production engineering we now take for granted.
Ampex and magnetic tape recording subsequently became a ubiquitous technology.