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We present an overview of four challenging research areas in multiscale physics and engineering as well as four data science topics that may be developed for addressing these challenges. We focus on multiscale spatiotemporal problems in light of the importance of understanding the accompanying scientific processes and engineering ideas, where "multiscale" refers to concurrent, non-trivial and coupled models over scales separated by orders of magnitude in either space, time, energy, momenta, or any other relevant parameter. Specifically, we consider problems where the data may be obtained at various resolutions; analyzing such data and constructing coupled models led to open research questions in various applications of data science. Numeric studies are reported for one of the data science techniques discussed here for illustration, namely, on approximate Bayesian computations.