  We construct the moduli space for equivalence classes of n-pointed tropical
curves of genus g, together with its compactification given by weighted
tropical curves, and establish some of its basic topological properties. We
compare it to the moduli spaces of smooth and stable algebraic curves, from the
combinatorial, the topological, and the Teichm\"uller point of view. The paper
is written in an expository style, and it generalizes some results contained in
sections 4-6 of arXiv:1001.2815v3.
