The IOP Homi Bhabha Lecture - A key recent focus in condensed matter physics attempts to related disparate many-body phenomena such as the glass transition in viscous liquids, jamming transition in granular materials and pinning transition in disordered elastic media. In all cases the single particle mobility of the systems vanishes. A simple relative of these complex many-body dynamics is the problem of the sticking of a Brownian colloid to a planar substrate immersed in a fluid which loses its mobility upon sticking. Using modern techniques such as an optical tweezer, combined with micro-positioning ability of scanning probe microscopes, one can investigate the crossover between non-glassy and marginally/minimally glassy dynamics in condensed matter in this pseudo-two body problem.