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Recently, topological phases in photonic and phononic systems have captured the attention of scientists and engineers. These topological phases are usually classified by integers, such as Chern numbers or winding numbers. We will use some examples to illustrate that we can have topological phenomena that are not characterized by integers. In the first example, we will see how non-Abelian topological charges (that behave like matrices) can be realized in some electromagnetic and acoustic systems; and the physical consequences that will arise, including the formation of boundary modes and the constraints on degeneracy features in the bulk. In the second example, we will see that some simple photonic/phononic crystals which do not have bulk integer topological invariants behave like a "valley-Hall" topological crystal when certain boundary conditions are applied. Although the transport phenomena are almost indistinguishable from the valley-locked transport in valley-Hall crystals, the underlying principle is based on a boundary-condition induced bulk chiral anomaly, which cannot be classified using the usual topological invariants.