Cepheids as distance indicators and stellar tracers

We review the phenomenology of classical Cepheids (CCs), Anomalous Cepheids (ACs) and type II Cepheids (TIICs) in the Milky Way (MW) and in the Magellanic Clouds (MCs). We also examine the Hertzsprung progression in different stellar systems by using the shape of I-band light curves (Fourier parameters) and observables based on the difference in magnitude and in phase between the bump and the minimum in luminosity. The distribution of Cepheids in optical and in optical-near infrared (NIR) color--magnitude diagrams is investigated to constrain the topology of the instability strip. The use of Cepheids as tracers of young (CCs), intermediate (ACs) and old (TIICs) stellar populations are brought forward by the comparison between observations (MCs) and cluster isochrones covering a broad range in stellar ages and in chemical compositions. The different diagnostics adopted to estimate individual distances (period--luminosity, period--Wesenheit, period--luminosity--color relations) are reviewed together with pros and cons in the use of fundamental and overtones, optical and NIR photometric bands, and reddening free pseudo magnitudes (Wesenheit). We also discuss the use of CCs as stellar tracers and the radial gradients among the different groups of elements (iron, alpha, neutron-capture) together with their age-dependence. Finally, we briefly outline the role that near-future space and ground-based facilities will play in the astrophysical and cosmological use of Cepheids.