Differential complexes are fundamental tools in geometry and analysis, encoding geometric structures through differential operators and cohomological invariants. In subRiemannian geometry, the classical de Rham complex is often replaced by more intrinsic subcomplexes, such as the Rumin complex, which better reflect the underlying graded structure. In this talk, I will discuss the problem of extracting differential subcomplexes adapted to Carnot groups and introduce a new family of complexes, called spectral complexes, arising from spectral sequence methods. I will present the construction of these complexes and outline some applications.