  The review of developed by the authors new techniques for covariant
calculation of matrix elements in QED, the so-called formalism of "Diagonal
Spin Basis" (DSB), is presented. In DSB spin 4-vectors of in- and out- fermions
are expressed just in terms of their 4-momenta. In this approach the little
Lorentz group, common for the initial and final states,is realized. This brings
the spin operators of in- and out-particles to coincidence. The developed
approach is valid both for massive fermions and for massless ones. There occur
no problems with accounting for spin flip amplitudes in it. Just 4-momenta of
particles participating in reactions are required in it to construct the
mathematical apparatus for calculations of matrix elements. We apply this
formalism to the next processes: 1) M\"oller and Bhabha bremsstrahlung
($e^{\pm}e^- \to e^{\pm}e^- \gamma$) in the ultrarelativistic limit when
initial particles and photon are helicity polarized; 2) Compton back-scattering
of photons of intensive circularly polarized laser wave on a beam of
longitudinally polarized ultrarelativistic electrons ($e+n\gamma_0 \to e+\gamma
$); 3) $e^+e^-$-pair production by a hard photon in simultaneous collision with
several laser beam photons ($\gamma+n \gamma_0 \to e^+ + e^-$); 4)
Bethe-Heitler process in the case of a linearly polarized photon emission by an
electron with account for proton recoil and form factors; 5) the reaction $ep
\to ep \gamma$ with proton polarizability being taken into account in the
kinematics when proton bremsstrahlung dominates; 6) orthopositronium 3-photon
annihilation ($e^+e^{-} \to 3 \gamma$).
