Many constructions built by ancient civilization hold many mysteries and attract the attention of historians, archaeologists and tourists from all over the world. The most famous and enigmatical among them is the Great (Khufu’s-Cheops’) Pyramid on the Giza plateau in Egypt. The assignment, construction methods and especially the inside structure of the Pyramid have been the cause of heated debate among historians and researchers since ancient times. Unfortunately, not only researchers are interested in ancient structures and excavation sites of archaeological values, but also robbers and illegal seekers of archaeological values. This led to the partial destruction of the Pyramid by the order of the Arab caliph Al-Ma’mun in the 9th century AD. From the middle of the last century, the point of view has prevailed that only non-destructive testing methods are acceptable when examining ancient structures. In the 1960s, a technology was proposed for transilluminating the pyramids of Giza by muons, which are generated by cosmic rays in the Earth’s atmosphere. This method gave promising results. Other means were also proposed, which include radar, as well as gravitational and vibration technologies. However, despite numerous attempts to use them, no significant success or discovery has been achieved. A discussion of these methods, their applications and partial successes is the subject of this article.