Three new methods for the detection and interception of frequency-hopped waveforms are presented. The first method extends the optimal, fixed-block detection method based on the likelihood ratio to a sequential one based on the Sequential Probability Ratio Test (SPRT). The second method is structured around a compressive receiver and is highly efficient yet easily implemented. The third method is based on the new concept of Amplitude Distribution Function (ADF) and results in a detector that is an extension of the radiometer. The first method presents a detector structured to make a decision sequentially, that is, as each data element is collected. Initially, a purely sequential test is derived and shown to require fewer data for a decision. A truncated sequential method is also derived and shown to reduce the data needed for a decision while operating under poor signal-to-noise ratios (SNRs). A detailed performance analysis is presented along with numerical and Monte Carlo analyses of the detectors. The second method assumes stationary, colored Gaussian interference and presents a detailed model of the compressive receiver. A locally optimal detector is developed via the likelihood ratio theory and yields a reference to which previous ad hoc schemes are compared. A simplified, suboptimal scheme is developed that trades off duty cycle for performance, and a technique for estimating hop frequency is developed. The performance of the optimal and suboptimal detectors is quantified. For the suboptimal scheme, the trade-off with duty cycle is studied. The reliability of the hop frequency estimator is bounded and traded off against duty cycle. In the third method, a precise definition of the ADF is given, from which follows a convolutional relationship between the ADFs of signal and additive noise. A technique is given for deconvolving the ADF, with which signal and noise components can be separated. A detection statistic characterized, yielding a framework on which to synthesize a detector. The detector's performance is analyzed and compared with the radiometer.