We propose a scenario where blazars are classified into flat-spectrum radio quasars (FSRQs), BL Lacertae (BL Lac) objects, low-synchrotron, or high-synchrotron peaked objects according to a varying mix of the Doppler-boosted radiation from the jet, the emission from the accretion disc, the broad-line region, and the light from the host galaxy. In this framework, the peak energy of the synchrotron power () in blazars is independent of source type and radio luminosity. We test this new approach, which builds upon unified schemes, using extensive Monte Carlo simulations, and show that it can provide simple answers to a number of long-standing issues, including, amongst others, the different cosmological evolution of BL Lac objects selected in the radio and X-ray bands, the larger values observed in BL Lac objects, the fact that high-synchrotron peaked blazars are always of BL Lac type, and the existence of FSRQ–BL Lac transition objects. Objects so far classified as BL Lac objects on the basis of their observed weak, or undetectable, emission lines are of two physically different classes: intrinsically weak lined objects, more common in X-ray-selected samples, and heavily diluted broad-lined sources, more frequent in radio-selected samples, which explains some of the confusion in the literature. We also show that strong selection effects are the main cause of the diversity observed in radio and X-ray samples, and that the correlation between luminosity and , which led to the proposal of the ‘blazar sequence’, is also a selection effect arising from the comparison between shallow radio and X-ray surveys, and to the fact that high-–high-radio-power objects have never been considered because their redshift is not measurable.