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.

我们回顾了银河系 (MW) 和麦哲伦云 (MC) 中的经典造父变星 (CC)、异常造父变星 (AC) 和 II 型造父变星 (TIIC) 的现象。我们还通过使用I波段光变曲线（傅里叶参数）的形状和基于光度凹凸与最小值之间的星等和相位差异的可观测值来检查不同恒星系统中的赫兹普鲁格级数。研究了造父变星在光学和光学-近红外（NIR）颜色-幅度图中的分布，以约束不稳定带的拓扑结构。通过比较观测值（MC）和覆盖广泛恒星年龄和化学成分的星团等时线，提出了使用造父变星作为年轻（CC）、中间（AC）和老年（T​​IIC）恒星群的示踪剂。回顾了用于估计个体距离（周期-光度、周期-Wesenheit、周期-光度-颜色关系）的不同诊断方法，以及使用基频和泛音、光学和近红外光度波段以及无红化伪星等的优缺点（我们）。我们还讨论了 CC 作为恒星示踪剂的用途，以及不同元素组（铁、 α、中子俘获）之间的径向梯度及其年龄依赖性。最后，我们简要概述了不久的将来空间和地面设施在造父变星的天体物理和宇宙学应用中将发挥的作用。