Strategic bombing was a new way of waging war in the Second World War, and required time and resources to mature. The German Luftwaffe in 1939 and 1940 began it (Warsaw, Rotterdam, and the Battle of Britain). The RAF had restrained itself from bombing German cities until May 1940.
British heavy bomber designs were more advanced than those of the Axis nations. A heavy bomber is a 'bomb truck' whose usefulness is ability to carry heavy loads for long distances, the versatility needed of medium bombers is unnecessary. However, the British soon learned that loss rates were too high if they attacked in daylight. After a year (1940-41) they found their accuracy at night was very poor as fewer than 50% of their bombs landed within three miles of their targets.
In 1941-2, the RAF slowly introduced Pathfinders (aircraft with excellent navigators) to mark target cities with flares at night, brought in better bombers and built up their strength.
In 1942, the US joined the offensive, but preferred to use heavy bombers like the B-17, which had heavy defensive armament and - as the theory went -- could reach the target in daylight if they flew in dense formations.
In 1943, the USAAF finally started bombing cities in Germany, but it was the British use of new radars (Oboe, H2S) that really alarmed Germany as the RAF was finally causing real destruction on the cities they attacked. The Hamburg Raids of August 1943 gutted much of the city and killed tens of thousands of people.
In 1944, the RAF raids could involve over 1,000 heavy bombers at night, and the USAAF would come with even more by day. A growing number of escort fighters and night-intruders also did much to lower the loss rate.
Just prior to D-Day the bombing campaign began to focus on two major targets: Railroad hubs, and Germany's synthetic oil plants. By late 1944 Germany lost an increasing amount of its railroad capacity and its war-machine ran low on fuel.
Germany -- particularly after 1943 --also pulled most of its fighter planes from the front lines to defend its cities, and needed tens of thousands of anti-aircraft guns for air defence. This made a significant difference on the battlefields on both fronts.
