  Cepheid stars are crucial objects for a variety of topics that range from
stellar pulsation and the evolution of intermediate-mass stars to the
understanding the structure of the Galaxy and the Universe through the distance
measurements they provide. The developments in hydrodynamical calculations, the
release of large ground-based surveys, and the advent of continuous,
space-based photometry revealed many puzzling phenomena about these stars in
the last few years. In this paper I collected some important and new results in
the topics of distance measurements and binarity investigations. I also
summarize the most recent discoveries in their light variations, such as period
doubling, modulation, low-amplitude additional modes, period jitter and the
signs of granulation, and discuss the new opportunities that current and future
space missions will offer for us.
