The concept of in-Memory Computing is nowadays a well-established principle. Instead of separating the processing device by the memory units, as usually done in traditional von Neumann architectures, it proposes new architectures based on memory devices providing simultaneous computing. Indeed, this keynote speech proposes the new concept of in-Memory Sensing and Computing as a disruptive novel approach in edge-computing. This novel concept is here proposed as based on the fusion of three architectural functions: sensing, computing and memorizing. This novel concept is proposed by using a simple architecture based on a single-kind of devices simultaneously providing these three functions: the memristors. The proposed novel approach also provides a breakthrough in cancer diagnostics. If fact, the concept is here demonstrated by showing a well-known case in oncology: the estimation of the risk of prostate cancer based on the measure of Prostate Specific Antigen (PSA) and its Membrane isoform (PSMA). So, this keynote discusses the first-ever-reported direct computation of the cancer risk on cancer markers detected with memristive biosensors simultaneously with the computation and data storing. Memristive biosensors are quite a novelty emerged in literature with first publications starting from 2011. These new kind of devices are of interest for many reasons but especially for their excellent Limit-of-Detection, which is down to the attomolar-ranges in cancer markers detection. They are often fabricated on silicon nanowires and manufactured with standard lithographic processes. This means the whole architecture may be CMOS-based and the biosensors themselves can be physically microfabricated onto the same dye. Therefore, this keynote talk opens to an important new area of research and development: the possibility to build innovative circuits and systems providing simultaneous sensing, computing, and storing for true lab-on-a-chip applications.