Emerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will include the necessity to operate over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider - shadowed fading, which contains as special cases the majority of the linear fading models proposed in the open literature. In particular, we propose an analytic framework to evaluate the average of an arbitrary function of the signal-to-noise-plus-interference ratio (SINR) over κ-μ shadowed fading channels by using a simplified orthogonal expression with tools from stochastic geometry. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, and outage probability of a K-tier HetNet with K classes of BSs, differing in terms of the transmit power, BS density, shadowing and fading. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities.