Today, smart materials are commonly used in various fields of science and technology, such as medicine, electronics, soft robotics, the chemical industry, the automotive field, and many others. Smart polymeric materials hold good promise for the future due to their endless possibilities. This group of advanced materials can be sensitive to changes or the presence of various chemical, physical, and biological stimuli, e.g., light, temperature, pH, magnetic/electric field, pressure, microorganisms, bacteria, viruses, toxic substances, and many others. This review concerns the newest achievements in the area of smart polymeric materials. The recent advances in the designing of stimuli-responsive polymers are described in this paper.