A two-dimensional (2D) topological insulator (TI) exhibits the quantum spin Hall (QSH) effect, in which topologically protected spin-polarized conducting channels exist at the sample edges. Experimental signatures of the QSH effect have recently been reported for the first time in an atomically thin material, monolayer WTe2. Electrical transport measurements on exfoliated samples and scanning tunneling spectroscopy on epitaxially grown monolayer islands signal the existence of edge modes with conductance approaching the quantized value. Here, we directly image the local conductivity of monolayer WTe2 devices using microwave impedance microscopy, establishing beyond doubt that conduction is indeed strongly localized to the physical edges at temperatures up to 77 K and above. The edge conductivity shows no gap as a function of gate voltage, ruling out trivial conduction due to band bending or in-gap states, and is suppressed by magnetic field as expected. Interestingly, we observe additional conducting lines and rings within most samples which can be explained by edge states following boundaries between topologically trivial and non-trivial regions. These observations will be critical for interpreting and improving the properties of devices incorporating WTe2 or other air-sensitive 2D materials. At the same time, they reveal the robustness of the QSH channels and the potential to engineer and pattern them by chemical or mechanical means in the monolayer material platform.