Spherical and circular microphone arrays and loudspeaker arrays are often used for the recording and reproduction of a given sound field. A number of approaches and formats are available for the representation of the recorded field, some of which are more popular among the audio engineering community (B-format, virtual microphones, etc.) whilst other representations are widely used in the literature on mathematics (generalized Fourier series, single layer potential, Herglotz wave function, etc.). In this paper, some of the properties of the various approaches and some of their differences are discussed. The analysis includes the representation of near-field sources and the choice of basis functions used for the representation.