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This note reviews complex and real techniques in harmonic analysis. Wedescribe a common source of both approaches rooted in the covariant transformgenerated by the affine group.  Keywords: wavelet, coherent state, covariant transform, reconstructionformula, the affine group, ax+b-group, square integrable representations,admissible vectors, Hardy space, fiducial operator, approximation of theidentity, maximal functions, atom, nucleus, atomic decomposition, Cauchyintegral, Poisson integral, Hardy--Littlewood maximal functions, grand maximalfunction, vertical maximal functions, non-tangential maximal functions,intertwining operator, Cauchy-Riemann operator, Laplace operator, singularintegral operator, SIO, boundary behaviour, Carleson measure.

The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform