Explore the connections between microscopic and macroscopic laws in physics through this comprehensive colloquium talk. Delve into the fundamental principles of heat conduction, Fourier's law, and the heat diffusion equation. Examine various approaches to proving Fourier's law, including kinetic theory and direct nonequilibrium measurements. Investigate heat conduction in disordered harmonic crystals, Anderson localization, and one-dimensional systems with non-integrable interactions. Discover signatures of anomalous transport and explore phenomenological descriptions like the Levy walkers model. Gain insights into fluctuating hydrodynamics, equilibrium simulations, and hydrodynamic theory for one-dimensional interacting systems. Conclude with a discussion on fluctuating hydrodynamics for a one-dimensional fluid and participate in a Q&A session to deepen your understanding of these complex physical phenomena.