This chapter analyzes the philosophical consequences of the recent discovery of direct violations of the time reversal symmetry of weak interactions. It shows that although we have here an important case of the time asymmetry of one of the fundamental physical forces which could have had a great impact on the form of our world with an excess of matter over antimatter, this asymmetry cannot be treated as the asymmetry of time itself but rather as an asymmetry of some specific physical process in time. The chapter also analyzes the consequences of the new discovery for the general problem of the possible connections between direction (arrow) of time and time-asymmetric laws of nature. These problems are analyzed in the context of Horwich’s (1987) argumentation, trying to show that existence of a time-asymmetric law of nature is a sufficient condition for time to be anisotropic. Instead of Horwich’s sufficient condition for anisotropy of time, it is stressed that for a theory of asymmetry of time to be acceptable it should explain all fundamental time asymmetries: the asymmetry of traces, the asymmetry of causation (which holds although the electrodynamic, strong, and gravitational interactions are invariant under time reversal), and the asymmetry between the fixed past and open future. It is so because the problem of the direction of time has originated from our attempts to understand these asymmetries and every plausible theory of the direction of time should explain them.