The biological response to biomaterials plays a crucial role in selecting suitable materials for the formulation and development of tissue engineering platforms. Biodegradation is one of the properties that is considered in selecting appropriate biomaterials for biomedical applications. Biodegradation is the process of breaking down large molecules into smaller molecules with/without the aid of catalytic enzymes. The biodegradation process is crucial in the chemical absorption, distribution, metabolism, excretion, and toxicity (ADMET) process of biomaterials and small molecules in the body. Degradation of biomaterials can be followed by assessing the physical, mechanical, and chemical attributes of biomaterials. There are several techniques/parameters that can be targeted when studying the degradation of biomaterials, with gravimetric analysis, surface erosion, and morphological changes being the largely employed techniques. However, the techniques present a few limitations, such as technical errors and material solubility being mistaken for degradation, and these techniques can infer but not confirm degradation as they do not provide the chemical composition of fragmenting/fragmented molecules. The American Society for Testing and Materials (ASTM) guidelines provide techniques and parameters for assessing biodegradation. However, the ASTM guidelines for degradation assessment approaches and techniques need to be updated to provide sufficient evidence to draw conclusive decisions regarding the degradation of biomaterials. In this review, the degradation assessment approaches and techniques are critically reviewed about their advantages and disadvantages, and to provide suggestions on how they can still play a role in assessing the degradation of biomaterials. This review could assist researchers employ cost-effective, efficient, and multiple degradation assessment techniques to evaluate and provide sufficient information about the degradation of biomaterials. Suggested future ASTM guidelines for assessing biodegradation should include measuring parameters (such as chemical, mechanical, or physical attributes of biomaterials) in real-time, employing non-invasive, continuous, and automated processes.