Unmanned aerial vehicles (UAVs), birds, and foreign objects near airport runways pose a serious threat to aviation safety, particularly during takeoff and landing phases, when aircraft operate at high speeds and low altitudes. Although drone-related incidents remain infrequent, they can cause significant disruptions, including costly flight delays and safety concerns. This paper presents a focused review of drone detection techniques, emphasizing the integration of Frequency-Modulated Continuous Wave (FMCW) radar and artificial intelligence (AI) methods—especially Convolutional Neural Networks (CNNs)—for UAV detection near runways. The article highlights the key benefits and limitations of these approaches in low-altitude, cluttered environments typical of airport infrastructure. Particular attention is given to the role of digital signal processing (DSP), including the use of Short-Time Fourier Transform (STFT) for extracting micro-Doppler signatures from radar echoes, which are subsequently analyzed by deep learning models. The review also outlines current research gaps, including the lack of real-world data and scenario-specific studies. The aim is to support the development of reliable UAV detection systems tailored to the unique challenges of runway surveillance.