In this talk, I will discuss a scenario for dark matter that has received some attention in recent years. It is based on particles with feeble --instead of weak-- interactions with the Standard Model. Hence the acronym FIMP, which stands for a feebly interacting massive particle. I will first discuss the status of the standard WIMP dark matter candidates and will argue, contrary to what the title may convey, that this paradigm is far from being excluded by current experiments. Then I will discuss in quite generic terms the FIMP scenario, with an emphasis on DM production mechanisms (including some new ones) and, also, on some possible experimental tests.