Device-to-device (D2D) communications are now considered an integral part of future 5G networks, which will enable direct communication between user equipments and achieve higher throughputs than conventional cellular networks, but with the increased potential for co-channel interference. The physical channels, which constitute D2D communications, can be expected to be complex in nature, experiencing both line-of-sight (LOS) and non-LOS conditions across closely located D2D pairs. In addition to this, given the diverse range of operating environments, they may also be subject to clustering of the scattered multipath contribution i.e., propagation characteristics which are quite dissimilar to conventional Rayleigh fading environments. To address these challenges, we consider two recently proposed generalized fading models, namely kappa-mu and eta-mu, to characterize the fading behavior in D2D communications. Together, these models encompass many of the most widely utilized fading models in the literature such as Rayleigh, Rice (Nakagami-n), Nakagami-m, Hoyt (Nakagami-q), and One-sided Gaussian. Using stochastic geometry, we evaluate the spectral efficiency and outage probability of D2D networks under generalized fading conditions and present new insights into the tradeoffs between the reliability, rate, and mode selection. Through numerical evaluations, we also investigate the performance gains of D2D networks and demonstrate their superiority over traditional cellular networks.