In World War II, anti-aircraft weapons became more advanced and deadly, as did the bomber forces they were intended to shoot down. While both Axis and Allies used anti-aircraft extensively, I would say the Germans were the best at it during this particular war. They certainly had lots of opportunity for practice.
The vast majority of anti-aircraft fire, also know as Flak, or "ack-ack" for the sound the guns made when on rapid fire, was on a time-delay fuse. This simply meant that the delay on the fuses could be adjusted depending on the altitude of the attacking force, the it was a simple physics and mathematical equation of leading the target and firing in a pattern.
When the time delay expired, the weapon exploded, and the most common kind simply sent shards of hot, shredded metal fragments in every direction, in hopes of slicing through airframe, fuselage, fuel tank and instruments, not to mention personnel. Allied airmen were terrified to be flying into a hail of German ack-ack without the ability to even turn away. It had to be the very definition of fear.
The 88mm gun (FlaK-36) used by the Germans was perhaps the most infamous and feared anti-aircraft gun of the war, though British and American models became quite good as well. Later versions used radar systems to calculate velocity of target and projectile, account for ballistics and send fire control commands to hydraulically-powered guns. The result was repeated and deadly volleys of flak that often found their targets. B-17s returning from a raid to England were often shot almost literally to pieces by these weapons.