Zero-Knowledge Proofs (ZKPs) have recently emerged as cutting-edge technologies capable of verifying the truthfulness of a statement without revealing any underlying information but only proving its correctness. This thesis takes a closer look at the study of ZKPs and in particular investigates the zk-STARK (Zero-Knowledge Scalable Transparent Arguments of Knowledge) protocol. It also studies the property of verifiable computation, analysing protocols in which this is combined with ZKP technologies. The main objective of this thesis is to realise and discuss the implementation of a software called VerComp, which simplifies and verifies the execution of software in server infrastructures. It allows even machines with reduced computational capacity to delegate the execution of applications to external servers and then obtain back ZKP proofs attesting to their correct execution.