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A well-known problem in algebraic geometry is to construct smooth projective Calabi--Yau varieties $Y$. In the smoothing approach, we construct first a degenerate (reducible) Calabi--Yau scheme $V$ by gluing pieces. Then we aim to find a family $f\colon X \to C$ with special fiber $X_0 = f^{-1}(0) \cong V$ and smooth general fiber $X_t = f^{-1}(t)$. In this talk, we see how infinitesimal logarithmic deformation theory solves the second step of this approach: the construction of a family out of a degenerate fiber $V$. This is achieved via the logarithmic Bogomolov--Tian--Todorov theorem as well as its variant for pairs of a log Calabi--Yau space $f_0\colon X_0 \to S_0$ and a line bundle $\mathcal{L}_0$ on $X_0$.