The estimate of concrete compressive strength is a major aspect in the assessment of reinforced concrete existing structures since it involves safety issues. The method of extracting concrete cores from the buildings under investigation is considered in this paper. In the first part, a brief review concerning procedures proposed by international technical codes as well methods available in the scientific literature, is made. In particular, formulations proposed for the determination of the actual concrete strength, starting from the one obtained from laboratory tests on cores, are examined. Special attention is devoted to the various factors affecting the estimate of the actual strength and relative correction coefficients. In the second part, the considered procedures are applied to a case study concerning a school building in Tuscany; comparison among different formulations allows some considerations on the reliability of the adopted procedures.