This is an interesting survey of the history of G. Higman’s PORC conjecture concerning the form of the function \(f(p^n)\) enumerating the number of groups of order \(p^n\). There are listed the cases in which Higman’s conjecture is confirmed. For example, all groups of order \(2^n\), \(n\leq 6\), were classified in full details many years ago (G. A. Miller, P. and M. Hall, J. K. Senior). Next, the PORC conjecture has been confirmed for \(n\leq 7\), for \(p\)-groups of class two. All \(p\)-groups of maximal class and order \(\leq p^7\) are classified. The author notes that the classification of groups of order \(p^8\) is extraordinarily difficult. The reader is suggested to read this informative survey of many related results.