The aim of this article is to present the current knowledge and experiences related to wear and fragmentation resistance tests and to indicate those of their aspects that require further research. For this purpose, a review of the literature was performed. Results show that tests of resistance to wear (the MDE/DS test) and fragmentation (the LA test) are performed worldwide according to different standards (and thus following different test methods), which prevents a comparison of the obtained results. Comparative research into the MDE/DS and LA tests indicates that the MDE/DS test is more effective. The disadvantage of both tests lies in the dimension range of the aggregate. In addition, the use of steel balls in the LA test may not reflect the actual influence that the internal properties of the material have on the fragmentation process. A final review of the available knowledge allowed the formulation of proposals regarding further research directions, such as proposed changes of test methods, extensive analysis, and selection of optimal dimensions for tested aggregates, analysis of short-term and long-term tests, as well as extensive research into and an analysis of the impact of crushing on the physical, mechanical, and geometric properties of aggregates.