The first RADAR patent was applied for by Christian Huelsmeyer on April 30, 1904 at the patent office in Berlin, Germany. He was motivated by a ship accident on the river Weser and called his experimental system "Telemobiloscope". In this chapter some important and modern topics in radar system design and radar signal processing will be discussed. Waveform design is one innovative topic where new results are available for special applications like automotive radar. Detection theory is a fundamental radar topic which will be discussed in this chapter for new range CFAR schemes which are essential for all radar systems. Target recognition has for many years been the dream of all radar engineers. New results for target classification will be discussed for some automotive radar sensors.