Properties of living and non-living matter, complex and often incomprehensible, seem to arise from a combination of only a few types of chemical bonds among atoms. One such `sp2 bond' among carbon atoms does wonders in simple graphene, a basic component of our pencil tip. Graphene, a two dimensional net of just carbon atoms, has caught the attention of physics community recently, through its surprising variety of quantum mechanical behavior. We will get a glimpse of the quantum complexity. After a review I will focus our own predictions of certain novel behavior in graphene, i) Lorentz contraction and time dilatation like phenomena , in a totally non-relativistic context and ii) 2 channel Kondo effect  and iii) room temperature superconductivity  in charged graphene.
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