Currently I'm consulting a project where R.C.C. casting is going on. Concrete cylinder sample is prepared on casting dates regularly. I have laboratory testing results of concrete which includes Density and Compressive strength. The project is to construct basement and semi-basement (underground) Radiation Shielding Concrete Room for Oncology Treatment rooms. So, concrete density and strength is the main parameters. The fresh concrete density is kept above 2.4 gram per in^2 and the hardened density should not fall below 2.35 gram per in^2. Coarse aggregates are 20mm and 12.5mm downgraded stone chips. PPC cement is used to prepare the concrete. If these specification satisfy your condition then I'll be able to help you with the average concrete strength after 28 days of casting.   

Do you mean the highest strength of concrete used in in actual building construction? If so, the answer seems to be concrete with compressive design strength of 300 N/mm2 design strength, which has been developed and used by Taisei Corporation in Japan. There is a brief mention about the building where the 300 N/mm2 concrete was used in the following URL:  http://www.taisei.co.jp/english/csr/annual_report_online2013/research.html

Taiheiyou Cement Corporation of Japan recently announced (in June 2015) that it has successfully developed a new cementitious material that delivers record compressive strength of  464 N/mm2 using normal pour-and-form techniques. (See http://www.taiheiyo-cement.co.jp/english/summary/pdf/150605.pdf). However, actual use in construction has not been reported yet and is probably many years away.

(There have been reports elsewhere that compressive strength of 673 N/mm2 using reactive powder concrete (RPC) technology has been achieved, but this requires curing of concrete under  high temperature and pressure (specifically, hot-press forming at 250°C to 400°C.)

http://www.taisei.co.jp/english/csr/annual_report_online2013/research.html

http://www.taiheiyo-cement.co.jp/english/summary/pdf/150605.pdf

Richard [1] reported that with curing at 90 °C in the conventional production mode, compressive strength of 280 MPa can be achieved. Also, he claimed that achieving compressive strengths as high as 550 MPa is possible if the curing temperature is increased to 250 °C. In an extreme case, curing in combined high pressure with 250 °C temperature can produce a concrete with a compressive strength of 810 MPa [1].

1.            Richard, P. Reactive Powder Concrete: A New-Ultra High Strength Cementitious Material. in Proceedings of the Fourth International Symposium on the Utilization of High-Strength/High-Performance Concrete. 1996. Paris, France.

achievements in  high strength concrete

really interesting answer Saheed

I agree with you Dr Amajd.