We propose channel estimation and direct equalization techniques for transmission over doubly selective channels. The doubly selective channel is approximated using the basis expansion model (BEM). Linear and decision feedback equalizers implemented by time-varying finite impulse response (FIR) filters may then be used to equalize the doubly selective channel, where the time-varying FIR filters are designed according to the BEM. In this sense, the equalizer BEM coefficients are obtained either based on channel estimation or directly. The proposed channel estimation and direct equalization techniques range from pilot-symbol-assisted-modulation- (PSAM-) based techniques to blind and semiblind techniques. In PSAM techniques, pilot symbols are utilized to estimate the channel or directly obtain the equalizer coefficients. The training overhead can be completely eliminated by using blind techniques or reduced by combining training-based techniques with blind techniques resulting in semiblind techniques. Numerical results are conducted to verify the different proposed channel estimation and direct equalization techniques.