A tutorial discussion on the receiving and scattering properties of antennas is presented. The objective of this work is to provide a comprehensive tutorial overview of the subject, in conjunction with circuit calculations and numerical simulations that illustrate the fundamental concepts of how antennas behave as both receivers and scatterers of electromagnetic fields and power. The paper begins with a discussion of the basic concepts associated with antenna impedance, as these are fundamental to understanding the antenna's receiving and scattering properties, particularly over a wide range of frequencies, where the circuit properties of the antenna differ. The definitions of aperture efficiency, absorption efficiency, and the validity of using either a Thevenin or Norton equivalent circuit to determine both received and total scattered power are discussed. Circuit circulations and numerical simulations, determining both total received and scattered powers, are presented for a number of antennas, including a straight-wide dipole, a circular loop, a reflector-backed dipole, and a Yagi antenna. We show that Thevenin and Norton equivalent circuits have limited validity when used to determine the total power scattered by a basic antenna element such as the dipole and loop. For the general antenna, these equivalent circuit models are not valid for determining the total scattered power.