Over the last decades, the progress made in the generation of laser pulses shorter than a picosecond (10^-12 s) has allowed us to reach extreme optical power intensities exceeding 10^15 W cm^-2. This tremendous power has triggered an abundance of original scientific and industrial applications. Chief amongst them is material processing, and in particular, in-volume processing of transparent materials, which motivates the present work. Femtosecond lasers induce a rich taxonomy of material modifications that can take diverse forms, including smooth densification, self-organised nanogratings, localised crystallisation, or amorphisation, that will vary in the processing parameter space, from one material to another. To date, effective methods for direct observation of laser-induced morphologies are missing. To address this need, this thesis work explores in situ methods for direct observation of femtosecond laser-modified zones. The first one consists in using a quantitative phase-contrast microscopy method: digital holographic microscopy. We propose a feedforward manufacturing method, which uses phase data acquired from the microscope to feed a semi-analytical model, a "digital twin". We demonstrate this resilience of this method to quill effects (directionality), and its increased inscription resolution. The second method consists in using full-field multiphoton microscopy. The interaction between the processing laser, with a decreased energy, and already-written structure, induces harmonics generation. Their signals and emission patterns change depending on the structures. Three different interaction regimes are identified in fused silica with third-harmonic generation, associated respectively with nanopores, nanogratings, and microexplosions. The former shows a correlation between the signal and wet etching rate. Full-field allows to identify the shape of the exposed modifications, and to study them by fast focal-plane tomography, highlighting their time-resolved formation. Finally, we present scientific demonstrations and potential applications for these methods. We show that we can inscribe large-scale refractive structures. We then show the validity of the incubation law, and highlight the stochastic nature of the interaction using the high contrast allowed by third-harmonic generation, with a survival analysis. We also show the ability of this method to detect otherwise optically undetectable laser-induced modifications, buried close to a surface. Finally, full-field third-harmonic generation microscopy allows to determine single-shot the nature of some modifications, particularly in the case of ultraviolet femtosecond laser processing.