Quantum mechanics stands unmatched in its experimental success. However, significant gaps remain in the quantum description of nature, notably the absence of a satisfactory integration of gravity and an unresolved measurement problem. This thesis investigates a potential approach to resolving these issues known as superdeterminism.

A superdeterministic theory is one which violates an assumption called Statistical Independence. Although this approach has historically been readily dismissed as harmful to science, superdeterminism has recently gained traction as researchers address these criticisms and explore its implications more deeply.

This thesis aims to provide a unified resource on superdeterminism, compiling progress, identifying current gaps, and suggesting future research directions. We establish criteria for evaluating superdeterministic theories and apply these to existing models. Our analysis focuses on two main approaches: the Donadi-Hossenfelder path integral approach and Palmer's Invariant Set Theory.

The path integral approach appears promising, particularly if a suitable measure for the "quantumness" of states can be developed. Invariant Set Theory provides a unique, geometric framework but is still too early in its development to show clear potential.

Our findings underscore the early stage of superdeterminism research and the need for further theoretical development and empirical testing. By providing a structured framework for future work, this thesis seeks to advance the understanding and application of superdeterminism in addressing the foundational issues in quantum mechanics.