Several difficult problems in complexity and cryptography can be stated as problems with tensors and hidden field equations Including quantum-resistance signature schemes of Blaser et. al., and cryptographic schemes of Patron and others. Many of these questions are in fact problems studied for independent reasons in the area of group isomorphism. For the past decade, several groups have leveraged linear algebra and Lie theory methods to make substantial practical and complexity breakthroughs on tensor computations. I will detail the these applications, summarize the results, and give a survey of the available methods.