We present a review of our theoretical calculations about magnon transport in quasi-one-dimensional (1D) magnonic circuits constituted by waveguides coupled to side resonators. Phenomena such as the existence of band gaps, rejective and selective transmissions and Fano resonances will be discussed as well as the applications of these structures in filtering and demultiplexing devices. The calculations are performed based on two types of models and in the frame of the Green's function method. First, the continuum long-wavelength Heisenberg model is studied in 1D monomode waveguide containing symmetric and asymmetric loops or coupled with grafted stubs. Then, we use the discrete dipole approximation in structures composed of a chain of nanometric magnetic clusters coupled to finite clusters on its vicinity. All such circuits exhibit a variety of interference effects in their transport properties which should have important consequences for designing integrated devices such as microwave filters