  Given two or more non-commuting observables, it is generally not possible to
simultaneously assign precise values to each. This quantum mechanical
uncertainty principle is widely understood to be encapsulated by some form of
uncertainty relation, expressing a trade-off between the standard deviations or
other measures of uncertainty of two (or more) observables, resulting from
their non-commutativity. Typically, such relations are coarse, and miss
important features. It was not until very recently that a broader perspective
on quantum uncertainty was envisaged and explored, one that utilises the notion
of an uncertainty region. Here we review this new approach, illustrating it
with pairs or triples of observables in the case of qubit and qutrit systems.
We recall some of the shortcomings of traditional uncertainty relations, and
highlight their inability to identify the full uncertainty region. These
shortcomings suggest a precautionary note that, we surmise, ought to accompany
the presentation of the uncertainty principle in introductory quantum mechanics
courses.
