I will start with the statistics indicating that the objects named in the title of my talk are either non-existing or very elusive to detect (not a single such object is known against 119 known Be/neutron star X-ray binaries). After brief reviewing of the properties of Be/X-ray binaries I discuss several objects that were proposed as the long sought for candidates for Be/black hole X-ray binaries. After three unsuccessful candidates (LS I +61° 303, LS 5039 and MAXI J1836-194), a successful candidate (AGL J2241+4454/MWC 656) was finally, very recently, announced.