We present a summary of what is currently known about the three distinct families of isolated pulsating white dwarfs. These are the GW Vir stars (He/C/O-atmosphere stars with Teff 120,000 K), the V777 Her stars (He-atmosphere, Teff 25,000 K), and the ZZ Ceti stars (H-atmosphere, Teff 12,000 K), all showing multiperiodic luminosity variations caused by low-order and low-degree g-mode instabilities. We also provide, in an Appendix, a very brief overview of the newly found evidence in favor of the existence of a fourth category of oscillating white dwarfs bearing strong similarities with these families of pulsators. We begin our survey with a short historical introduction, followed by a general discussion of pulsating white dwarfs as compact pulsators. We then discuss the class properties of these objects, including an updated census. We next focus on the instability domains for each family of pulsators in the log g - Teff diagram, and present their time-averaged properties in more detail. This is followed by a section on excitation physics, i.e., the causes of the pulsational instabilities, with emphasis on the common properties of the different types of pulsator. We then discuss the time-dependent properties of the pulsating white dwarfs featuring, among other things, a brief "picture tour" across the ZZ Ceti instability strip. We next review the methods used to infer or constrain the angular geometry of a pulsation mode in a white dwarf. These include multicolor photometry and time-resolved spectroscopy, the exploitation of the nonlinear features in the observed light curves, and rotational splitting. We also consider basic adiabatic asteroseismology starting with a discussion of the reaction of the period spectrum to variations of model parameters. We next review the various asteroseismological inferences that have so far been claimed for white dwarfs. We also discuss the potential of exploiting the rates of period change. We finally provide some concluding remarks, including a list with several suggestions for future progress in the field.