The distributed inference framework comprises of a group of spatially distributed nodes which acquire observations about a phenomenon of interest. Due to bandwidth and energy constraints, the nodes often quantize their observations into a finite-bit local message before sending it to the fusion center (FC). Based on the local summary statistics transmitted by nodes, the FC makes a global decision about the presence of the phenomenon of interest. The distributed and broadcast nature of such systems makes them quite vulnerable to different types of attacks. This paper addresses the problem of secure communication in the presence of eavesdroppers. In particular, we focus on efficient mitigation schemes to mitigate the impact of eavesdropping. We present an overview of the distributed inference schemes under secrecy constraints and describe the currently available approaches in the context of distributed detection and estimation followed by a discussion on avenues for future research.