The time-tested BCS theory of superconductivity is generally accepted to be the correct theory of conventional superconductivity by physicists and, by extension, by the world at large. There are, however, an increasing number of `red flags' that strongly suggest the possibility that BCS theory may be fundamentally flawed. An ever-growing number of superconductors are being classified as `unconventional', not described by the conventional BCS theory and each requiring a different physical mechanism. In addition, I argue that BCS theory is unable to explain the Meissner effect, $the$ most fundamental property of superconductors. There are several other phenomena in superconductors for which BCS theory provides no explanation. Furthermore, BCS theory has proven unable to predict any new superconducting compounds. This paper suggests the possibility that BCS theory itself as the theory of `conventional' superconductivity may require a fundamental overhaul. I outline an alternative to conventional BCS theory proposed to apply to all superconductors, `conventional' as well as `unconventional', that offers an explanation for the Meissner effect as well as for other puzzles and provides clear guidelines in the search for new high temperature superconductors.