Soft Condensed Matter (SCM) is a broad area of science, which includes studying liquids, colloids, gels, polymers, foams, biomaterials, etc. The common feature shared by all SCM materials is the energy associated with their behavior, which is comparable with the ambient thermal energy. With the development of new instrumental and modeling base, SCM faces discoveries of new phenomena, and consequently, new challenges of their understanding. In this talk, I will describe several of such challenges, and focus on two of them, the challenges we came across recently. The first challenge is the understanding of abnormally slow diffusion in silica nanochannels (nanotubes). Molecular motion, diffusion in well defined nanoscale geometry is of interest not only from fundamental point of view (transport in biological channels, the properties of interfacial water, capillary of rocks in geophysics, etc.), but also from the applied point of view (catalysis, molecular sensing, and controlled drug delivery). To study the molecular diffusion in a single silica nanochannel, we used recently synthesized arrays of silica nanochannels (ASNC). Studying diffusion of fluorescent organic molecules in those 3nm channels, we found that the coefficient of diffusion is ~108 times smaller than in water. Several possible explanations of nature of this phenomenon will be discussed. The second challenge is in finding the nature of an unusual molecular layer around the surface of human cervical cancer cells. Processing force data collected with atomic force microscopy (AFM), we derived the existence of an effective short and dense surface layer, which was unique for cancerous cells. The discovery of a new physical feature of cancerous cells opens not only a novel way of looking at the fundamental cellular changes associated with cancer, but also shows a possible non-traditional way for cancer detection. A few such methods of detection will be described. The estimated accuracy of the detection by means of these just pure physical methods was substantially higher compared to the existing biomedical methods. This makes it interesting to perform a detailed further study of the nature of the found layer.