In this talk, we will present what are known as "zeroizing attacks" against two candidate constructions of cryptographic multilinear maps, namely [GGH13] and [CLT13] (with an emphasis on the latter).  We will then discuss recent attempts at recovering from these attacks, both by modifying the mathematical construction of the multilinear maps to prevent zeroizing attacks, and by examining what forms of obfuscation can still be achieved in the presence of zeroizing attacks.