This study presents the information and conclusions about numerous tests – destructive and non-destructive – on concrete core specimens. The main focus is made on basic tests namely density test, water absorption test, rebound hammer test, ultrasonic pulse velocity test, and compression test. All test aim to provide us a comprehensive and sufficient data for assessing the „quality‟ and „strength‟ of concrete core specimens. The details all the necessary and essential points commencing from the preparation of core specimens, as per various nationally and internationally accepted design codes for concretes, ranging from procedures of tests, leading to final conclusions and findings of core strength and quality and their correlations. Comparative study of block concrete pavements and in-situ concrete pavements are briefly made and their strengths and quality are assessed. Basic requirements for ideal core dimensions are also explained. Also, two specimen cores from PCCBP (Plastic Cell filled Concrete Block Pavement) were tested for density test and water absorption test. Their inferences are also mentioned in conclusion section of the study.