In recent years, a relatively large number of publications in journals of high-level citations (Nature, etc.) showed that compounds with hydrogen under pressure could become superconducting up to room temperature. In my talk, I am going to summarize some of those results and of the problems that exist with the published data. One key issue several authors of those high-citation-index papers did not take into account, is granular superconductivity, a phenomenology expected for inhomogeneous superconductors. For example: an anomalous field hysteresis in the magnetoresistance, or the possibility of producing a permanent current in the sample after decreasing an applied magnetic field to zero. Not all these features were fully demonstrated in compounds with hydrogen under pressure, but they were published in the last 15 years in pure graphite samples. Several of these results will be summarized in the talk, indicating the existence of superconductivity with critical temperature around 350K or even above it, as recent reports from laboratories in France indicate. Theoretical work and experimental facts suggest that superconductivity is located at certain two-dimensional stacking faults (interfaces), which most of highly oriented graphite samples in a certain proportion have. I will also shortly discuss recently published results partly obtained at CCNH/UFABC.

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