Thermal conductivity (k) plays an essential role in functional devices. In some cases, high value is required to transfer heat efficiently. In others, low k assists in maintaining a temperature gradient necessary for device operation. It is profitable to design materials where one can tune k in a broad range according to its function. Beyond functionality, k is a fundamental property of matter, and a fantastic probe to assess vibrational dynamics and electronic structure in condensed matter. In conjunction with other transport properties such as electrical resistivity and thermoelectric power, k promotes a deeper understanding of the electronic and vibrational structure of materials. In the present Thesis, careful experimental determination of the transport coefficients of a variety of systems over a broad temperature range (4-300 K) let me unveil subtle interactions between phonons and/or electrons. The insights gained from an accurate interpretation of these properties empowers us to engineer and fine-tune the functionality of materials for applications. I first investigate the thermoelectric properties of nickel-based high-entropy alloys (HEAs), believed to host unconventional effects arising from the high level of site-disorder in their crystalline structure. Anomalous resistivity with a low temperature coefficient validates the disordered nature of HEAs. The Seebeck coefficient, reported for the first time for HEAs, is surprisingly low. In the quest to understand transport in HEA, I have discovered that iron-nickel alloys exhibit a promising thermoelectric figure of merit (ZT) of 0.1 at room temperature. One way to further increase ZT is to decrease k (in FeNi alloys or other materials) by texturing the material. Aluminium foams are systems of choice to observe the effect of a modified structure on the thermoelectric properties. Tailoring of the bubbles' size is demonstrated by applying an external acoustic force in the foaming process. Moreover, the influence of the macro- and micro- structure of the foams on thermoelectric properties is discussed. The best example for tuning k by texturing it is anatase titanium dioxide (TiO2). k was varied over three orders of magnitude by adjusting its oxygen contents and by texturing it into a foam, aerogel-like structure. We identified a new, strong diffusion mechanism of heat by polarons, created as a consequence of oxygen vacancies. Furthermore, anatase nanowires organized into foams result in an unprecedented low k = 0.014 W/Km at room-temperature. Doping this anatase foam heralds promising applications, in particular in thermoelectricity. An oxide which has an intrinsically nanoporous structure reminding that of a foam, is Mayenite (Ca12Al14O33). The thermal conductivity of such system is verified to be intrinsically low. The peculiar cage structure could host atomic of molecular species to tune its electrical conductivity, with bright prospects for thermoelectric applications. Finally, the thermoelectric properties of hybrid halide perovskites, cheap and easy-to-synthesise compounds, were studied. Three materials of this family have ultra-low k, due to the vibrational degrees of freedom of their organic cations. Notably, a tin-based organic-inorganic compound delivers ZT = 0.13 at room temperature. The thermoelectric conversion efficiency of this material was measured directly and is believed to yield promising thermoelectric applications.