  I study several aspects of tests of macrorealism (MR), which for a given data
set serves to give a quantitative signal of the presence of a specific notion
of non-classical behaviour. The insufficiency of classical understanding
underpins both the paradoxes of quantum mechanics, its future technological
promise, and so these tests are of interest both foundationally and
pragmatically. I derive generalisations of the Leggett-Garg (LG) inequalities
and Fine's theorem, which together establish the necessary and sufficient
conditions for macrorealism. First, I extend these conditions to tests
involving an arbitrary number of measurement times. Secondly, I generalise them
beyond the standard dichotomic variable, to systems described by many-valued
variables. I also perform a quantum mechanical analysis examining the interplay
of different conditions of MR. I then develop the theoretical framework to
support tests of macrorealism in continuous variable systems, where I define
variables based on coarse-grainings of position. I calculate temporal
correlators for general bound systems, and analyse LG violations within the
quantum harmonic oscillator (QHO), in its energy eigenstates and coherent
states. I analyse the precise physical mechanisms underpinning the violations
in terms of probability currents, Bohm trajectories. Staying within continuous
variable systems, we outline a different approach to meeting the invasiveness
requirement of LG tests. Reasoning that we may approximately non-invasively
measure whether a particle crosses the axis, we measure an object which is
related to the standard correlators, and derive a set of macrorealistic
inequalities for these modified correlators. We demonstrate violations of these
modified LG inequalities for several states within the QHO.
