The field of stimuli-responsive polymers has grown in the past three decades from a few obscure examples to one of the most vibrant domains of modern macromolecular science. Indeed, the research, development, and implementation of tailored materials that can respond in predefined ways to specific stimuli now cut across most areas in which "traditional" polymers play a role, and an ever-growing range of commercial products benefits from this class of materials. This Perspective is devoted to multistimuli, multiresponsive (MSMR) polymers, which are those materials that are able to respond to multiple, different stimuli with multiple, distinct responses. Somewhat akin to living systems, which have evolved to adapt and respond in complex ways to (combinations of) different environmental cues, MSMR polymers can offer a broad range of complex properties and functions. While much of the work on MSMR polymers has been devoted to the investigation of solutions or gels, this Perspective concentrates on solid materials, as this is the state of matter in which the vast majority of polymers are currently employed. In a tutorial fashion, an outline of some of the most common mechanisms used to implement stimuli-responsive behavior in polymer solids is provided. To convey a glimpse of the potential and the challenges of these general design principles, select examples of materials that display multistimuli, single-response as well as single-stimulus multiresponse behavior are presented, before polymeric materials that are truly multistimuli, multiresponsive are discussed, and an outlook on possible directions that future work in the field may take is presented.