In this chapter, we explore singularities in logarithmic geometry in more depth than we did in the introduction. We discuss, with some additional examples, our notion of a generically log smooth family and their log de Rham complexes. We investigate the base change property and the log Gorenstein property of generically log smooth families in some detail. We review our construction of elementary log toroidal families from toric data and define log toroidal families as generically log smooth families whose log singularities are locally modeled on elementary log toroidal families. We end the chapter by reviewing the Hodge–de Rham degeneration for proper log toroidal families over a log point.