In this study, we apply interferometric microscopy to study the phase, alongside the intensity, of the light field transmitted through a wide variety of samples. Additionally, we conduct those interferometric measurements at different wavelengths within the visible spectrum, probing the spectral evolution of the optical effects that the studied samples create. Using a priori knowledge about the samples, we identify specific features and trends they imprint on the parameters of the transmitted field, thus we optimally analyze the recorded intensity and phase data. We demonstrate that phase maps include useful information that reveal the features of the samples. The wide applicability of the spectrally resolved interference microscopy is the major novelty contributed by the present work. The phase seldom recorded, therefore we first present and explain the tools that we use throughout this work, both in terms of set-up and data post-processing. Next, we show the acquired results, starting from samples with typical dimensions in the few hundreds of microns and concluding with particles of few hundreds of nanometers. More specifically, we study microlenses of high numerical aperture that are difficult to characterize with conventional methods. We propose a novel approach to extract the surface profile of such microlens, providing useful feedback for manufacturing purposes. We do that by using phase measurements at a plane that lies between the surface of the lens and its focal plane. The next sample we study is a phase element, which is naturally easier to discern in the phase domain. We localize specific points in intensity and phase profiles that are correlated to the position of the walls of the actual sample. We also demonstrate the existence of phase singularities in phase measurements that can be proved an invaluable tool in high precision characterization processes. Next, we investigate the photonic nanojet phenomenon, which is the bright spot created on the shadow side of a dielectric sphere. The creation of this bright spot is not achieved through propagation inside the material, like conventional lenses, it is the combination of the light scattered and diffracted by the sphere. Therefore, we study its spectral evolution using intensity measurements and outline the size of the sphere that indicates the crossing from the dominant refractive regime to the diffractive one; combining intensity and phase information, we attempt to identify the size at which the behavior of the dielectric spheres changes again from diffractive to scattering. In the last experiments chapter, we study individual nano-sized particles, which are either simple spheres (dielectric / metallic) or the more complex structures of the core-shell meta-atom. We show that the spectral information of their response in intensity and phase can be used to identify the particle itself (simple dielectric / metal or meta-atom) and assess its responses with the respect to the engineered one (for the meta-atom case). Those examples validate the claimed benefits of the phase exploration. Still, there is ample room for further study; we debate about those prospects in the concluding chapter of this work.