A compact graph-like space is a triple (𝑋,𝑉,𝐸), where 𝑋 is a compact, metrizable space, 𝑉⊆𝑋 is a closed zero-dimensional subset, and 𝐸 is an index set such that 𝑋⧹𝑉≅𝐸×(0,1). New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta.