We review the local model for the log singularities of toric log Calabi–Yau spaces in the Gross–Siebert program. They are examples of elementary log toroidal families arising from a specific construction. Then, we define log toroidal families of Gross–Siebert type as log toroidal families whose log singularities are modeled on the local models arising from the aforementioned construction. Some of the local models have particularly simple log singularities; we say that they are “unisingular.” In the unisingular case, Gross and Siebert proved that unisingular generically log smooth deformations are locally rigid. In the final section of this chapter, we review their proof. This gives us a means to construct systems of deformations in many situations and thus confirms that our theory based on systems of deformations is meaningfully more general than log smooth deformation theory.