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The existence of Dark Matter is widely accepted in the scientific community, but its identity is still an enigma. Numerous independent gravitational observations seen cannot be explained by the Newtonian mechanics of the visible mass. A rather simple hypothesis suggests the existence of new particle or particles, termed as Dark Matter, to give a rationale for these observations. This paper seeks to give a comprehensive overview on the existing theories of dark matter candidates and the status of the dark matter search. This review begins with a description of the Standard Model of Elementary Particles followed by a brief discussion on the principle problems unexplained by this model. We then compare the theoretical predictions with the actual galactic rotation curve of the Andromeda Galaxy and its scientific implications, supporting the claim that dark matter exists. We investigate the prominent dark matter models including WIMPs, Axions, and Sterile Neutrinos, critically examining each of their theoretical motivations, production mechanisms, characteristics, and interactions with the standard model. We also explore a wide range of their direct and indirect detection methods- particle colliders, astronomical observations and data, advanced detectors, and many more- in detail. Furthermore, we give the reader insights into selective experiments being conducted that claim to give possible signals of dark matter. We conclude our paper with a discussion of contemporary and upcoming experiments to detect dark matter. Future experimentation will be critical to the development of this field. Old and new candidates will inevitably be ruled-out and developed as dark matter theory and detection methods continue to progress forward.