We consider a version of the Solow growth model where technological progress can be investment specific or investment neutral. The labour market is subject to search frictions, and the existing productive units may fail to adopt the most recent technological advances. Technological progress can lead to the destruction of technologically obsolete jobs and cause unemployment. We calibrate the model to replicate the high persistence that characterizes the dynamics of firms' neutral technology and the frequency of firms' capital adjustment. We find that neutral technological advances increase job destruction and job reallocation and reduce aggregate employment. Investment-specific technological advances reduce job destruction, have mild effects on job creation, and are expansionary. Hence, neutral technological progress prompts Schumpeterian creative destruction, while investment-specific technological progress operates essentially as in the standard neoclassical growth model. Using structural VAR models, we provide support to the key dynamic implications of the model.