  The Event Horizon Telescope (EHT) Collaboration recently published the first
images of the supermassive black holes in the cores of the Messier 87 and Milky
Way galaxies. These observations have provided a new means to study
supermassive black holes and probe physical processes occurring in the
strong-field regime. We review the prospects of future observations and
theoretical studies of supermassive black hole systems with the next-generation
Event Horizon Telescope (ngEHT), which will greatly enhance the capabilities of
the existing EHT array. These enhancements will open up several previously
inaccessible avenues of investigation, thereby providing important new insights
into the properties of supermassive black holes and their environments. This
review describes the current state of knowledge for five key science cases,
summarising the unique challenges and opportunities for fundamental physics
investigations that the ngEHT will enable.
