In a plethora of random models for constraint satisfaction and statistical inference problems, researchers from different communities have observed computational gaps between what existential or brute-force methods promise, and what known efficient algorithms achieve. In this talk, I will discuss this phenomenon in the context of the so-called Group Testing problem. Group Testing is a fundamental problem in statistical inference with many real-world applications. The goal is to detect a set of k defective items out of a population of size p using n