Between WWI and WWII, several air power proponents made huge claims that just didn't stand up to reality. There were claims that "the bomber would always get through" and "air power alone could cripple an enemy's ability and will to fight". As absurd as they sound in retrospect, those are actual quotes from the era.

WWII proved both of these claims wrong. Radar allowed the British to intercept German bombers during the Battle of Britain. Many bombers did not get through. Despite killing over 20,000 British citizens, German bombing didn't cause their will to crack. Churchill summarized their attitude was "give it 'em back!" Those WWII Brits were made of sturdy stuff.

The same held true when the British and later the Americans bombed Germany. They stopped many bombers although they didn't manage to completely stop an air raid. Despite the attacks, many of their critical industries like fighter production actually saw an increase during the war. The most effective bombing campaign against the Germans really came when we had such overwhelming numbers that the raids couldn't be stopped, when radar allowed bombing even in bad weather, and when critical industries like oil production were effectively targeted.

The situation in Japan was somewhat different. Logistics and distances made bombing Japan very difficult. B-29 bombers, when flown as intended at high altitude, encountered the Jet Stream which made bombing accuracy difficult. It wasn't until LeMay ordered a switch to medium altitude night firebombing attacks that an effective bombing campaign became possible.

After the war, extensive studies were conducted on the effectiveness of aerial bombardment. These studies showed serious flaws in bombardment as conducted in the war and lead credance to the "air power doesn't work" claims.

The situation wasn't improved very much with Korea and Vietnam. There weren't very many strategic targets to hit so the heavy bombers were frequently used to support tactical objectives.

Late in the Vietnam war, the first laser guided bombs entered service. These bombs made it possible for a single plane to take out difficult targets (like bridges) that whole squadrons had trouble hitting before. This was the beginning in the revolution of bombing accuracy we see today. Combine this technology with things like GPS guided bombs, stealth aircraft that can precisely aim at their targets without having to worry about evasive actions, standoff bombing (glide bombs) technology, etc., with an effective strategy and you can have a very effective bombing campaign. All of these are recent developments, good for us and very bad for our enemies.