Emerging memory systems such as resistive random access memory (RRAM), phase-change memory (PCM), and spin-transfer torque magneto-resistive random access memory (STT-MRAM) offer unique physical properties useful in designing next-generation processing in-memory (PIM) circuits and systems. Modified dynamic random access memory (DRAM) designs are also demonstrating on-chip data processing and bulk data operation capabilities. However, in-memory computation can fundamentally change the security models and assumptions of existing systems due to several key factors, such as modified system architecture, disparate programming models, side-channel effects, device reliability, hardware Trojans, and malicious perturbations in data processing. Therefore, in this paper, we survey and examine fundamental vulnerabilities arising from processing-in-memory systems. We aim to present the PIM system architects and designers an overview of security issues that can jeopardize the future of in-memory computation.