  This note is mostly an expository survey, centered on the topology of
complements of hyperplane arrangements, their Milnor fibrations, and their
boundary structures. An important tool in this study is provided by the degree
1 resonance and characteristic varieties of the complement, and their tight
relationship with orbifold fibrations and multinets on the underlying matroid.
In favorable situations, this approach leads to a combinatorial formula for the
first Betti number of the Milnor fiber and the algebraic monodromy. We also
produce a pair of arrangements for which the respective Milnor fibers have the
same Betti numbers, yet are not homotopy equivalent: the difference is picked
up by isolated torsion points in the higher-depth characteristic varieties.
