The authors study the notion of openness for continuous maps of locales, and various weakenings thereof, with particular attention paid to the interpretation of these weaker conditions in the spatial case. In particular, they rediscover the result (published independently by the reviewer in [Manuscr. Math. 31, 217-247 (1980; Zbl 0433.18002)] and by \textit{H. Dobbertin} in [Math. Z. 187, 13-21 (1984; Zbl 0523.06017)]) that open maps of spatial locales coincide with open maps of spaces if the range space is a \(T_ D\)-space. Since the main virtue of the paper is its encyclopaedic nature, it is a pity that they do not include Dobbertin's counterexample to show that this equivalence need not hold when both domain and range spaces are sober.