The no-hair theorem asserts that uncharged black holes are described by the Kerr solution, however, there is no evidence that spacetime geometry around Sagittarius A*, a compact radio source at the center of the Milky Way, is really described by this metric. Very strong evidence suggests that Sagittarius A* marks the position of a super massive black hole and its proximity in combination with its huge mass makes its apparent event horizon as seen from Earth, the largest of any black hole candidate in the universe and therefore, it presents a unique opportunity to observe strong-field general relativity effects. In the following years, very long baseline interferometry (VLBI) facilities will be able to directly image the accretion flow around the black hole candidate at the center of the Milky Way, and resolve the silhouette predicted by general relativistic lensing. Hence, the possibility of testing the nature of astrophysical black hole candidates with current and future observations has recently become an active research field. On the other hand, alternative theories of gravity provide with many examples of rotating non-Kerr black hole geometries that differ from the general relativity solution in the number of parameters needed to describe them and in some physical properties, as for example the trajectories of particles moving around them. In particular, the existence of an accretion structure around the black hole may provide not only the particles for testing the geodesics around the black hole, but also provides a source of photons that will be affected by the gravitational field too. In this work, we will investigate how the observation of the shadow of a black hole and the spectrum of an accretion structure around it, may provide an estimate for the parameters characterising Kerr and non-Kerr black holes and hence, giving us some tools to distinguish one from the other. In order to obtain this objective, we will use the power of computation to simulate images and spectra of a toroidal accretion structure in the vicinity of a black hole as seen from different points in space. We will develop a code to simulate the relevant physical processes of emission and absorption in the accretion structure and to incorporate them in a radiative transfer equation to obtain a realistic spectrum. Then, within the 3+1 formalism of general relativity we will use an adequate ray-tracing code to numerically integrate the geodesic equations for the photons produced by the accretion structure, introducing relativistic effects such as lensing and gravitational redshift. Hence, our code will provide us not only the images of the accretion structure around the black hole but also the expected spectrum for different observers. In order to obtain high resolution images and spectra in a reasonable computation time we want to acquire a high performance machine, that will be used by our research group in subsequent works. Finally, we want to clarify that the M.Sc. theses proposed in this project will be the first step in a long term research program. Hence, although our code will be capable of treating a general class of metrics, in this part of the work we will focus on the regular black holes geometries arising from considering smeared mass distributions, obtained by our group in a recent paper. Here we will concentrate in the study of the relation between the spin of the black hole and the parameter determining the size of the smeared mass distribution by observing the apparent shape of the shadow and the images and spectra of the accretion structure as seen from an asymptotic observer. Then, using some astronomical observables, as for example those defined by Hioki and Maeda (2009), and applying our results to the particular case of Sagittarius A*, we will characterise our images to find a criterion to distinguish Kerr and non-Kerr black holes by direct observation.