This 1965 article explores the inherent complexities and potential pitfalls in using radioactive decay to establish absolute ages for geological materials. The article systematically examines numerous dating methods, including variations of the lead-uranium and lead-thorium techniques, the helium method, the strontium method, argon-potassium dating, and carbon-14 dating. For each method, Acrey outlines the fundamental principles and assumptions, as well as the practical challenges and potential sources of error. The article highlights issues such as the loss or addition of parent and daughter isotopes through processes like leaching and diffusion, the variability of initial isotope ratios, the potential for contamination from external sources, and uncertainties in the decay constants. Acrey emphasizes the importance of critically evaluating the geological context of samples and integrating multiple dating techniques to mitigate potential errors and arrive at more reliable age estimates. The article underscores the inherent limitations of absolute age determination methods and calls for cautious interpretation of results in light of these complexities