Nowadays there are many gloomy prophecies provided by both technologists and economists about the detrimental effects of the so-called Fourth Industrial Revolution on aggregate employment and its composition. These prophecies imply that in the near future we will face Robocalypse - a massive replacement of people by machines alongside an explosion in joblessness. This paper provides theoretical, empirical and historical evidence that the phenomenon of technological unemployment is a phantom. The most general results can be summarized as follows: in the long run, reduction in labor demand under the impact of new technologies is merely a theoretical possibility that has never before been realized in practice; at the level of individual firms, there is a strong positive relationship between innovations and employment growth; at the sectoral level, technological changes cause a multidirectional employment response, since different industries are at different stages of the life cycle; at the macro level, technological progress acts as a positive or neutral, but not a negative factor; a surge in technological unemployment, even in the short-term, seems a remote prospect since in coming decades the pace of technological change is unlikely to be fast enough by historical standards; the impact of new technologies on labor supply may be a more serious problem than their impact on labor demand; technological changes seem to have a much greater effect on the composition of employment than on its level.