Recent years have seen unprecedented excitement, both in experiments and theory, in the arena of soft and granular matter under various driving fields. These studies provide new paradigm in non-equilibrium physics, cutting across different disciplines like physics, biology and chemical engineering. My talk will cover some examples from our ongoing experiments. The first example will be colossal shear thickening in very dilute suspensions of carbon nanotubes. We have demonstrated a discontinuous shear-thickening transition on varying shear stress where the viscosity jumps sharply by five orders of magnitude in flocculated suspensions of multiwalled carbon nanotubes (MWNT) at very low weight fractions (~ 0.5%). An understanding of the shear-thickening phenomena is pertinent for designing smart materials like soft body armors and shock absorbers. Colloidal polycrystals under shear reveal deep insights into grain growth mechanisms via preferential kinetic roughening and anisotropic enhancement of particle mobilities. A polar granular rod subjected to vertical oscillations in a medium of non-polar particles shows interesting dynamics. A collection of active particles show spontaneous circulatory motion seen for cells and locusts.