  The central theme of this thesis is the study and analysis of black hole
mimickers. The concept of a black hole mimicker is introduced, and various
mimicker spacetime models are examined within the framework of classical
general relativity. The mimickers examined fall into the classes of regular
black holes and traversable wormholes under spherical symmetry. The regular
black holes examined can be further categorised as static spacetimes, however
the traversable wormhole is allowed to have a dynamic (non-static) throat.
Astrophysical observables are calculated for a recently proposed regular black
hole model containing an exponential suppression of the Misner-Sharp
quasi-local mass. This same regular black hole model is then used to construct
a wormhole via the ''cut- and-paste'' technique. The resulting wormhole is then
analysed within the Darmois-Israel thin-shell formalism, and a linearised
stability analysis of the (dynamic) wormhole throat is undertaken. Yet another
regular black hole model spacetime is proposed, extending a previous work which
attempted to construct a regular black hole through a quantum ''deformation''
of the Schwarzschild spacetime. The resulting spacetime is again analysed
within the framework of classical general relativity. In addition to the study
of black hole mimickers, I start with a brief overview of the theory of special
relativity where a new and novel result is presented for the combination of
relativistic velocities in general directions using quaternions. This is
succeed by an introduction to concepts in differential geometry needed for the
successive introduction to the theory of general relativity. A thorough
discussion of the concept of spacetime singularities is then provided, before
analysing the specific black hole mimickers discussed above.
