In this paper, we survey recently proposed methods for protecting against side-channel and fault attacks in shared FPGAs. These methods are quite versatile, targeting FPGA compilation flow, real-time timing-fault detection, on-chip active fences, automated bitstream verification, etc. Despite their versatility, they are mostly designed to counteract a specific class of attacks. To understand how to address the problem of security in shared FPGAs in a comprehensive way, we discuss their individual strengths and weaknesses, in an attempt to identify research directions necessitating further investigation.