The date of Mycobacterium tuberculosis complex emergence has been the subject of long debates. New studies joining archaeological efforts with sequencing methods raise high hopes for solving whether this emergence is closer to 70,000 or to 6000 years before present. Inferring the date of emergence of this pathogen based on sequence data requires a molecular clock. Several clocks inferred from different types of loci and/or different samples, using both sound reasoning and reliable data, are actually very different, which we refer to as the paradoxes of M. tuberculosis molecular evolution. After having presented these paradoxes, we will remind the limits of the molecular clocks used in the different studies such as the assumption of homogeneous substitution rate. We will then review recent results that shed new light on the characteristics of M. tuberculosis molecular evolution: traces of diverse selection pressures, the impact of host dynamics, etc. We provide some ideas on what to do next to get nearer to a reliable dating of Mycobacterium tuberculosis complex emergence. Among them, the collection of additional remains from ancient tuberculosis seems still essential.