## 1 Introduction  
The study of the propagation of light in highly scattering media has great importance in a wide range of applications (biological media, pharmaceutical, food, wood) [1; 2; 3; 4; 5; 6]. Over the last decade, advancements in instrumentation and novel methods of analysis and methodologies have fostered innovation and breakthroughs in diffuse optical spectroscopy (DOS) [7; 8; 9]. In particular, probing human tissue with light brings in a slew of benefits thanks to non-invasiveness, the potential for compact bedside or wearable monitoring, and cost-effective solutions [10; 11; 12]. That makes diffuse optics an attractive tool to explore the human body in vivo [12; 13; 14; 15]. To harvest maximum benefit, various practical implementation approaches have been developed by the scientific community. Typically, the measurement scheme includes a light source and a detector placed at a known distance, and the acquired data are processed using diffusion models to extract the optical properties (absorption, scattering) of the medium under investigation. The continuous wave (CW) approach uses CW light sources to estimate optical properties [16; 17; 18; 19]. Thus, only light attenuation is measured. This approach is easier to implement and cost-effective. However, it suffers from the coupling between absorption and scattering properties that cannot be independently evaluated from a single measurement. The solution to the coupling could be found by adding another dimension to the measurement. That can be achieved performing CW measurements at multiple source-detector distances or a different approach: frequency domain (FD) and time domain (TD): frequency domain (FD) and time domain (TD) acquire photon propagation in diffusive media at multiple frequency and time, respectively [20; 21; 22; 23; 24]. Both approaches naturally disentangle the absorption and scattering coupling. The time domain approach has the advantage of gating photons at a different time of arrival, thus enabling depth segmentation of diffusive media based on the concept that longer propagation times allow photons to reach deep within the medium. In vivo applications of diffuse optics are mostly explored in the therapeutic window (600-1100 nm), where light attenuation in human tissues is comparatively low [25; 26; 27; 28]. Furthermore, quantification of tissue constituents (chromophores) can be performed through the Beer-Lambert law, by a linear fit of typical tissue constituent absorption spectra with the broadband absorption spectrum of in vivo tissue [29; 30]. Information on the microscopic structure, useful for tissue characterization, can also be derived from the scattering properties. Over the years, broadband diffuse optical spectroscopy using the above-mentioned approaches has been explored by various scientific communities across various applications, which, as mentioned initially, range from human tissue, to food, wood, pharmaceutical, and other [28; 31; 32; 33; 34; 35]. This review will focus on the broadband time domain approach to diffusive media, henceforth named as time domain diffuse optical spectroscopy (TD-DOS). Unlike few wavelength time domain systems, broadband TD-DOS has the unique advantage of resolving an extended spectral range along with inherent benefits of depth segmentation using time gating and uncoupling of absorption from scattering. It is thus an ideal tool for exploration studies, where the key features of the tissue under study are understood, and the results, in turn, are exploited to create few wavelengths (typically smaller, cheaper, and simpler) dedicated systems [27; 36; 37; 38; 39]. With the advent of new technologies, the complexity of time domain instruments has been reduced from laboratory to compact devices, portable on wheels [23; 27; 36; 40]. For the light source, bulky Ti:Sapphire lasers have been replaced by compact supercontinuum sources [41; 42].