In this talk, we review recent developments towards the calculation of multi-loop scattering amplitudes.
In particular, we discuss how the colour-kinematics duality can provide new integral relations at one-loop level
via the Loop-Tree duality formalism.
On the other hand, in order to compute scattering amplitudes at one- and two-loop level,
numerically and analytically, we describe
the preliminary automation of the adaptive integrand decomposition algorithm.
We show preliminary results on the analytic reduction of the $\mu e$-elastic scattering at one- and two-loop level.