The dynamics and radiation of ultrarelativistic electrons in strong counterpropagating laser beams are investigated. Assuming that the particle energy is the dominant scale in the problem, an approximate solution of classical equations of motion is derived and the characteristic features of the motion are examined. A specific regime is found with comparable strong field quantum parameters of the beams, when the electron trajectory exhibits ultrashort spike-like features, which bears great significance to the corresponding radiation properties. An analytical expression for the spectral distribution of spontaneous radiation is derived in the framework of the Baier-Katkov semiclassical approximation based on the classical trajectory. All the analytical results are further validated by exact numerical calculations. We consider a non-resonant regime of interaction, when the laser frequencies in the electron rest frame are far from each other, avoiding stimulated emission. Special attention is devoted to settings when the description of radiation via the local constant field approximation fails and to corresponding spectral features. Periodic and non-periodic regimes are considered, when lab frequencies of the laser waves are always commensurate. The sensitivity of spectra with respect to the electron beam spread, focusing and finite duration of the laser beams is explored.
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