We review the history and status of the famous classification of extraterrestrial civilizations given by the great Russian astrophysicist Nikolai Semenovich Kardashev, roughly half a century after it has been proposed. While Kardashev's classification (or Kardashev's scale) has often been seen as oversimplified, and multiple improvements, refinements, and alternatives to it have been suggested, it is still one of the major tools for serious theoretical investigation of SETI issues. During these 50+ years, several attempts at modifying or reforming the classification have been made; we review some of them here, together with presenting some of the scenarios which present difficulties to the standard version. Recent results in both theoretical and observational SETI studies, especially theĜ infrared survey (2014)(2015), have persuasively shown that the emphasis on detectability inherent in Kardashev's classification obtains new significance and freshness. Several new movements and conceptual frameworks, such as the Dysonian SETI, tally extremely well with these developments. So, the apparent simplicity of the classification is highly deceptive: Kardashev's work offers a wealth of still insufficiently studied methodological and epistemological ramifications and it remains, in both letter and spirit, perhaps the worthiest legacy of the SETI "founding fathers".