In this talk, we consider the structure and spectral properties for commuting pairs of bounded linear operators acting on a Hilbert space which are a correct extension of the structure and spectral properties of single bounded linear operators. We also define and investigate operator transforms such as generalized spherical Aluthge and mean transforms for commuting pairs of bounded linear operators. It is well-known that the spectral and invariant subspace properties of single bounded linear operators are preserved under generalized Aluthge transforms. In the last part of our series of talks, we study the invariance properties of Taylor spectra using Koszul complexes and joint invariant subspaces for commuting pairs of bounded linear operators under generalized spherical Aluthge and mean transforms.