A classical problem in algebraic geometry is the construction of smooth projective Calabi-Yau varieties, in particular of mirror pairs. In the approach via smoothings, the first step is to construct a reducible Gorenstein Calabi-Yau variety (or a pair thereof) by closed gluing of simple pieces. The second step is to find a family of Calabi-Yau varieties whose special fiber is the already constructed reducible Calabi-Yau variety, and whose general fiber is smooth. Logarithmic geometry, and especially logarithmic deformation theory, has given new impulses to the second step of this approach. In particular, the logarithmic version of the Bogomolov-Tian-Todorov theorem implies the existence of smoothings. This talk has two parts. In the first part, I will give an introduction to the logarithmic perspective on degenerations and smoothings of varieties with illustrated slides. In the second part, I will delve deeper into certain aspects of deformation theory and the Bogomolov-Tian-Todorov theorem.