Since the no-scalar-hair theorems of the 1970s, it has long been thought that four-dimensional, asymptotically flat black holes cannot support any kind of non-minimally coupled real scalar hair, if not for the controversial Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole. However, the 2010s have seen renewed interest in the healthy, higher-order scalar-tensor theories which were described by Horndeski in 1974, and easily escape the assumptions of the no-hair arguments. Up to now, all analytic, asymptotically Newtonian black hole solutions in these higher-order theories assumed some symmetry for the scalar-tensor theory. In the present seminar, we start from a class of Horndeski actions which do not possess any symmetry, and which include typical potentials arising from Kaluza-Klein dimensional reduction of higher-dimensional theories. In spherical symmetry, we establish integrability and compatibility conditions bearing on these generalized potentials. For such actions respecting these compatibility conditions, black holes with secondary hair are then obtained, including black holes with Schwarzschild-like asymptotics, whose important properties are discussed. The selected scalar-tensor theories do not present any symmetry. Rather, they appear to be the sum of two Lagrangian densities: one which is conformally invariant in five dimensions (but not in four), the other which is explicitly related to a Kaluza-Klein reduction of Einstein-Gauss-Bonnet theory.