Dear readers, this issue of the journal Thermal Science contains-11 papers employing the Goodman heat-balance integral method (HBIM) in solution of variety of problems. The idea to create this collection came to my mind in 2007 when I solved a specific problem pertinent to heat transfer problems of the fire boilover - see Thermal Science, Vol. 11 (2007), Issue 2. Even though the method is simple and almost 50 years old, the problem solved and the solution outcomes encouraged me to do a deep look what was published for 50 years. The result of this was astonishing amount of articles employing directly or to some extent the HBIM. In the journals of Elsevier, for example, there were published of 450 articles approximately employing this amazing method. Then, the idea to create a special issue dedicated to the 50th anniversary of the Goodman method was realized and approved by the Editor-in-Chief. The collection of articles was not easy but finally, I am glad that the dream came true. In fact this special issue is a unique collection of articles devoted to HBIM ever created for 50 years since the seminal Goodman article in 1958.