Communication over fading interference channels in the presence of statistical quality of service (QoS) constraints is considered. Effective capacity, which provides the maximum constant arrival rate that a given service process can support while satisfying statistical queueing constraints, is employed as the performance metric. In a two-user and buffer constrained setting, arrival rate regions that can be supported in the fading interference channel are studied. More specifically, for three different strategies, namely treating interference as noise, time division with power control and simultaneous decoding, achievable throughput regions are determined. It is demonstrated that as in Gaussian interference channels, simultaneous decoding expectedly performs better (i.e., supports higher arrival rates) when interfering links are strong, and treating interference as noise leads to improved performance when the interfering cross links are weak while time-division strategy should be preferred in between. When the QoS constraints become more stringent, it is observed that the sum-rates achieved by different schemes all diminish and approach each other, and time division with power control interestingly starts outperforming others over a wider range of cross-link strengths.