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Simple wave oscillations in plasmas can produce enormous effects. This talk first explains what is a plasma wave. I then focus on two recently discovered, curious, and potentially useful effects, both mediated by the plasma wave, and both involving wave compression. One effect is resonant Raman backscattering, whereby a long moderately intense laser beam loses its energy to a short counter-propagating beam, producing a much shorter and much more intense pulse. This effect might overcome the material limitations of present technology, enabling the next generation of laser intensities. A second compression effect occurs when the plasma itself is compressed; not only does its temperature increase, but any embedded waves might also increase in energy. For adiabatic changes in time of the density of the plasma medium, the coherent wave energy grows, but, importantly, might then very abruptly lose this energy.