We present an ensemble of recent observational results on molecular clouds which, taken separately, could all be understood by invoking various unrelated physical processes, but taken all together form a coherent ensemble stressing the imprints of turbulence in the physics of the cold interstellar medium. These results are first, the existence of wings in the molecular line profiles, which can be interpreted on statistical grounds as the signature of the intermittency of the velocity field in turbulent flows, second the fractal geometry of the cloud edges, with properties reminiscent of those of various surfaces studied in turbulent laboratory flows, and third, the fact that the dense gas fills only a very small fraction of the space. The last points are supported by CO multitransition observations of a few fields in nearby molecular clouds. They show that the excitation conditions are the same for the gas emitting in the linewings and in the linecores and are also remarkably uniform over a large range (factor 10) of column densities. An attractive interpretation of the molecular line data is that most of the 12CO(J=2—1) and (J=3—2) emissions arise in cold (Tk ≥ 10K) and dense (nH2 ∼ 104 cm —3 or more) structures distributed on a fractal set with no characteristic scale size greater than about 1000 AU.