An attempt to answer the puzzling question, "Can we observe galaxies that recede faster than light ? ", has led to a re-examination of the notions of time, distance, velocity and redshift as they occur in Newtonian Physics, Special Relativity, General Relativity and Cosmology. It is found that these basic notions have different meanings in the different contexts, that once the differences are recognized, paxticularly those between Special Relativity and Cosmology, the above question becomes straightforward and easily answered. It is pointed out that what is interesting to physics is not individual events, but intervals between specified events. A sequence of key equations and expressions highlights the transition from one theoretical frame to the next. A number of common misconceptions are pointed out. It is underlined that modern cosmology is not pure General Relativity; rather, it is an application of General Relativity under the Cosmological Principle, thanks to which quantities relating to large distances at given times become well-defined and calculable.