We present an approach to study the interaction between matter and evanescent fields. The approach is based on the decomposition of evanescent plane waves into multipoles of well-defined angular momentum transverse to both decay and propagation directions. We use the approach to identify the origin of the recently observed directional coupling of emitters into guided modes, and of the opposite Zeeman state excitation of atoms near a fiber. We explain how to rigorously quantify both effects, and show that the directionality and the difference in excitation rates grow exponentially with the multipolar order of the light-matter interaction. We also use the approach to study and maximize the transverse torque exerted by an evanescent plane wave onto a given spherical absorbing particle. The maximum occurs at the quadrupolar order of the particle, and for a particular polarization of the plane wave. All the obtained physical insights can be traced back to the two main features of the decomposition of evanescent plane waves into transverse multipolar modes: A polarization independent exponential dominance of modes with large transverse angular momentum, and a polarization controlled parity selection rule.