  A tournament is unimodular if the determinant of its skew-adjacency matrix is
$1$. In this paper, we give some properties and constructions of unimodular
tournaments. A unimodular tournament $T$ with skew-adjacency matrix $S$ is
invertible if $S^{-1}$ is the skew-adjacency matrix of a tournament. A spectral
characterization of invertible tournaments is given. Lastly, we show that every
$n$-tournament can be embedded in a unimodular tournament by adding at most $n
- \lfloor\log_2(n)\rfloor$ vertices.
