  We review the original approach to the Le-Murakami-Ohtsuki (LMO) invariant of
closed 3-manifolds (as opposed to the later approach based on the Aarhus
integral). Following the ideas of surgery presentation, we introduce a class of
combinatorial structures, called Kirby structures, which we prove to yield
multiplicative 3-manifold invariants. We illustrate this with the
Reshetikhin-Turaev invariants. We then introduce a class of combinatorial
structures, called pre-LMO structures, and prove that they give rise to Kirby
structures. We show how the Kontsevich integral can be used to construct a
pre-LMO structure. This yields two families of multiplicative 3-manifolds
invariants $\{\Omega_n^{\mathfrak{c}}\}_{n\geq 1}$ and
$\{\Omega_n^{\mathfrak{d}}\}_{n\geq 1}$. We review the elimination of redundant
information in the latter family, leading to the construction of the LMO
invariant. We also provide uniqueness results of some aspects of the LMO
construction. The family of invariants $\{\Omega_n^{\mathfrak{c}}\}_{n\geq 1}$
is not discussed explicitly in the literature; whereas
$\Omega_n^{\mathfrak{c}}$ enables one to recover $\Omega_n^{\mathfrak{d}}$ for
any $n \geq 1$, we show that these invariants coincide for $n = 1$.
