  An oriented tree $T$ on $n$ vertices is unavoidable if every tournament on
$n$ vertices contains a copy of $T$. In this paper we give a sufficient
condition for $T$ to be unavoidable, and use this to prove that almost all
labelled oriented trees are unavoidable, verifying a conjecture of Bender and
Wormald. We additionally prove that every tournament on $n + o(n)$ vertices
contains a copy of every oriented tree $T$ on $n$ vertices with polylogarithmic
maximum degree, improving a result of K\"uhn, Mycroft and Osthus.
