Some aspects of discounting of infinite streams of economic quantities (consumption, saving, utility) are considered. The main points of the paper may be summarized as follows. The philosophy of discounting concerns methods of evaluation and/or comparison of multi-period phenomena and processes. The techniques applied (numerical, analytical) may equalize the gravity of subsequent generations or privilege certain generations rather than other ones. They can – to some extent – influence quality of life and the chances of survival in future generations. These (quite natural) connections between discounting and intergenerational justice and sustainability have been pointed out. Systems of axioms for “ethical” and “sustainable” preferences are presented, together with some related (sub)disciplines. Inspirations derived mainly from psychology suggest the modification of the geometric discounting paradigm by slowing down the convergence of discount factors to zero. It should be pointed out that such “heavy tailed” discounting has proved to be useful (and become strongly recommended) for evaluation of a variety of long-time horizon undertakings. Some examples of non-classical discounting rules are given. Finally, the author’s proposal of modeling the duration of the world as a Poisson random variable has been formulated.