Extended Abstract#br# Waveform is the information carrier for radar sensing. It is transmitted in some relatively fixed patterns in traditional architectures, which makes it difficult to further enhance the integrated sensing capacity of radar by relying only on adaptive processing at the receiver end. Cognitive waveform optimization based on target, jamming, and clutter characteristics revolutionizes the classical idea of ambiguity-function based waveform design and promises to radically boost sensing performance in complex environment. Compared with the rapid development of signal processing for receivers, cognitive waveform optimization for transmitters is still in its infancy. In this paper, we systematically summarize the theoretical foundations, basic frameworks, and related system advances in cognitive waveform optimization. Second, single-radar-mission oriented criteria and methods are summarized and analyzed in terms of detection, tracking, imaging, classification, and anti-jamming, and a comprehensive survey of related research progress is provided, which offers a longitudinal comparative perspective for single-radar-mission oriented cognitive waveform optimization. Then, starting from the key information required for different target cognitive levels as well as taking into account the coupling between different radar missions, we progressively analyze the similarities and differences of their corresponding criteria and methods, which offers a horizontal comparative perspective for joint-radar-mission oriented cognitive waveform optimization. Finally, we analyze several major challenges to further improve the integrated sensing capacity of cognitive radars, and point out some research topics that are worth focusing on, including the effectiveness evaluation of environment knowledge, general performance measurement criteria of waveform, intelligent cognitive waveform design, and efficient real-time optimization techniques.#br#