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“What are some German inventions and innovations that occurred during WWII?”There are many inventions and innovations made by Germans in WW2. I will write only about the most important one:Principles of modern aerodynamic in the high subsonic and transonic regime.The very first results were presented already in 1935 at Volta Conference by Adolf Busemann. Just to be mentioned, NACA was very conservative. Let's see what is stated in Wikipedia:“In February 1945, NACA engineer Robert T. Jones started looking at highly swept delta wings and V shapes, and discovered the same effects as Busemann. He finished a detailed report on the concept in April, but found his work was heavily criticised by other members of NACA Langley, notably Theodore Theodorsen, who referred to it as "hocus-pocus" and demanded some "real mathematics".[4] However, Jones had already secured some time for free-flight models under the direction of Robert Gilruth, whose reports were presented at the end of May and showed a fourfold decrease in drag at high speeds. All of this was compiled into a report published on June 21, 1945, which was sent out to the industry three weeks later.[10] Ironically, by this point Busemann's work had already been passed around.”Germans built also first transonic wind tunnel at Junkers to study the aerodynamic in transonic regime. So called Area Rule, later called Whitcomb Area Rule after it was re-invented in 1952 by Richard T. Whitcomb, were invented and patented in 1944 by Otto FrenzelJunkers patent drawing from March 1944Fundaments of modern RocketryGermans built the very first modern ballistic rocket V2 (American notation V-2), predecessor of modern liquid fuel rockets. When the first information reached the Britain, the brave scientist denied the possibility of liquid fuel rocket engine as there is no pump with the necessary capacity to be airborne. The father of this rocket Werner von Broun later work in USA. What say Wikipedia“As Germany collapsed, teams from the Allied forces—the United States, the United Kingdom, and the Soviet Union—raced to capture key German manufacturing sites and technology. Werner von Braun and over 100 key V-2 personnel surrendered to the Americans and many of the original V-2 team ended up working at the Redstone Arsenal. The US also captured enough V-2 hardware to build approximately 80 of the missiles. The Soviets gained possession of the V-2 manufacturing facilities after the war, re-established V-2 production, and moved it to the Soviet Union.”A U.S. Army cut-away of the V-2Passive IR homingGermans were working on IR seekers throughout from the 1930 and a result culminated in Zielgerät 1229 Vampir riflescope. Less know is their work on passive homming. They started with theoretical works:“Aware of the advantages of passive IR homing, the research program started with a number of theoretical studies considering the emissions from the targets. This led to the practical discovery that the vast majority of the IR output from a piston engine aircraft was between 3 and 4.5 micrometres. The exhaust was also a strong emitter, but cooled rapidly in the air so that it did not present a false tracking target.[13] Studies were also made on atmospheric attenuation, which demonstrated that air is generally more transparent to IR than visible light, although the presence of water vapour and carbon dioxide produced several sharp drops in transitivity.[14] Finally they also considered the issue of background sources of IR, including reflections off clouds and similar effects, concluding this was an issue due to the way it changed very strongly across the sky.[15] This research suggested that an IR seeker could home on a three-engine bomber at 5 kilometres (3.1 mi) with an accuracy of about ​1⁄10 degree,[16] making an IR seeker a very desirable device.”Germans developed at least two working IR homing system, Hamburg for fire-and-forget anti-shipping attacks mounted on gliding bomb BV 143 and Madrid for surface-to-air guided missiles.“The Kepka Madrid system had an instantaneous field of view (IFOV) of about 1.8 degrees and scanned a full 20 degree pattern. Combined with the movement of the entire seeker within the missile, it could track at angles as great as 100 degrees. Rheinmetall-Borsig and another team at AEG produced different variations on the spinning-disk system.”The Madrid seeker was being developed for the Enzian surface-to-air missile.Germans made different SA guided missiles beside Enzian shown in the bottom pictureA Rheintochter R1 (left), and part of an R3 (centre), with a Rheinbote (right).However, this SA missiles were never used in defence, but the basic concept of passive IR homing was later used in more developed form in well-known Sidewinder AA rocket.Radar technicsI see, all readers think RADAR was British invention. They are wright if we think that the radar is microwave devices, working in SHF range (1 – 10 cm, 3 – 30 GHz). But the EM radiation in this range is strongly absorbed by atmosphere and is not suitable for early warning radars. At the beginning of WW2 Germans had much better radar technics, working in the VHF range (1 – 10 m, 30 – 300 MHz), an order of magnitude shorter wavelengths than British counterpart, Chain Home working oh HF range (10 – 100 m, 3 – 30 MHz). There was such a gap between the knowledge on both sides of the Channel that German even at the beginning didn’t know what these huge antenna towers for 12 m radio waves on the coast were.Freya (right) and Würzburg-Riese, date and place unknownCompare the German one like a radar still today with Chain Home radar towers bearing no similarity with the present-day radar.Chain Home radarIn 1944 they introduced the very first phased array long range early warning radar FuMG 41/42 Mammut which can detect aircraft flying at 8000 m on the fascinating range of 300 km.“At the same time, the GEMA in Germany built the Mammut 1.[14] It was later adapted for radio astronomy leading to Nobel Prizes for Physics for Antony Hewish and Martin Ryle after several large phased arrays were developed at the University of Cambridge. This design is also used for radar, and is generalized in interferometric radio antennas.”Mammut pased array radar antennaGermans were not only strong on this giant early warning radars but also in passive radar homing. The most knows were FuG 227 Flensburg which was developed to home night fighters onto VHF Monica tail warning radar installed on RAF bombers. Flensburg was used only for a short time since the Monica was complete disaster causing increased losses and was removed after a month or two.The second well known passive radar homing device was suited to detect S and X band British (H2S) and US (H2X) radars. There were many variants of FuG 350 Naxos & FuG 351 Korfu for airborn, maritime and land use. Generally, Luftwaffe was aware of RAF or USAAF air raid even before the pilots were briefed for the mission. Monica and H2S radars must be warmed up on the ground and Germens were easily detect the emission...That’s about some German inventions during the WW2 which are in use even today, however in more developed form.PS: I didn’t' give links to the Wikipedia pages I cited, it is easy to find it.