We reconsider the nonlocal aspects of quantum mechanics with special reference to the EPR argument. We first confine our considerations to the correlations between the outcomes of measurements on spatially distant constituents, without worrying about the measurement problem. We pay particular attention to the relativistic aspects of the problem. Our first conclusion is that, when developed along the lines we follow, the EPR inference that quantum correlations and locality together imply incompleteness, is appropriate. We then investigate whether the other common (...) conclusion from the EPR argument, i.e. that standard quantum theory implies a spooky action at a distance, is correct. We emphasize the crucial role played by the locality assumption and we discuss the use of counterfactuals in the ‘relativistic’ reformulation of the EPR argument. We show that the above conclusion is false if understood as saying that standard quantum theory exhibits, at least with reference to possessed elements of physical reality, some sort of parameter dependence. Thus, in a sense, the coexistence of quantum mechanics with relativity is even more peaceful than commonly thought. We then go through a similar analysis by taking explicitly into account the measurement process. We point out the difficulties which one meets when confronting reduction mechanisms with relativistic requirements. This leads us to recognize the necessity of reconsidering the criteria for attributing objective properties to individual physical systems. Our final conclusion is that, in principle, it is perfectly possible to build up theories leading to the objectification of macroscopic properties which do not imply any spooky action at a distance. (shrink)