A total dominator coloring of a graph $$G$$ G is a proper coloring of the vertices of $$G$$ G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number $$\chi _d^t(G)$$ χ d t ( G ) of $$G$$ G is the minimum number of colors among all total dominator coloring of $$G$$ G . A total dominating set of $$G$$ G is a set $$S$$ S of vertices such that every vertex in $$G$$ G is adjacent to at least one vertex in $$S$$ S . The total domination number $$\gamma _t(G)$$ γ t ( G ) of $$G$$ G is the minimum cardinality of a total dominating set of $$G$$ G . We establish lower and upper bounds on the total dominator chromatic number of a graph in terms of its total domination number. In particular, we show that every graph $$G$$ G with no isolated vertex satisfies $$\gamma _t(G) \le \chi _d^t(G) \le \gamma _t(G) + \chi (G)$$ γ t ( G ) ≤ χ d t ( G ) ≤ γ t ( G ) + χ ( G ) , where $$\chi (G)$$ χ ( G ) denotes the chromatic number of $$G$$ G . We establish properties of total dominator colorings in trees. We characterize the trees $$T$$ T for which $$\gamma _t(T) = \chi _d^t(T)$$ γ t ( T ) = χ d t ( T ) . We prove that if $$T$$ T is a tree of $$n \ge 2$$ n ≥ 2 vertices, then $$\chi _d^t(T) \le 2(n+1)/3$$ χ d t ( T ) ≤ 2 ( n + 1 ) / 3 and we characterize the trees achieving equality in this bound.