We consider 1-way quantum finite automata (QFAs). First, we compare the set of languages recognized by QFAs with the set of languages recognized by their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFA can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with a smaller probability are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. We construct a 1-way QFA that is exponentially smaller than any equivalent classical (even probabilistic) finite automaton.