Theoretical considerations lead to the expectation that stars should not have masses larger than about $m_{\rm max*}=60$–$120M_\odot$, while the observational evidence has been ambiguous. Only very recently has a physical stellar mass limit near $150M_\odot$ emerged thanks to modern high-resolution observations of local star-burst clusters. But this limit does not appear to depend on metallicity, in contradiction to theory. Important uncertainties remain though. It is now also emerging that star-clusters limit the masses of their constituent stars, such that a well-defined relation between the mass of the most massive star in a cluster and the cluster mass, $m_{\rm max}={\cal F}(M_{\rm ecl}) \le m_{\rm max*}\approx 150M_\odot$, exists. One rather startling finding is that the observational data strongly favour clusters being built-up by consecutively forming more-massive stars until the most massive stars terminate further star-formation. The relation also implies that composite populations, which consist of many star clusters, most of which may be dissolved, must have steeper composite IMFs than simple stellar populations such as are found in individual clusters. Thus, for example, $10^5$ Taurus–Auriga star-forming groups, each with 20 stars, will ever only sample the IMF below about $1M_\odot$. This IMF will therefore not be identical to the IMF of one cluster with $2\times 10^6$ stars. The implication is that the star-formation history of a galaxy critically determines its integrated galaxial IMF and thus the total number of supernovae per star and its chemical enrichment history. Galaxy formation and evolution models that rely on an invariant IMF would be wrong.