Resolution of singularities is one of the central and difficult problems in algebraic geometry. To date, most general approach to this problem is via algorithm in nature. In this talk, we will present a gentle discussion on resolution of singularities via possible geometric methods.  As it is known, many moduli spaces possess arbitrary singularities. In other words, singularities exist for certain geometric reason. Our idea is to modify the boundary of a given moduli by adding suitable additional objects, inducing natural modular blowups. This approach will be explained, using the moduli of quotients (i.e., Grothendieck's Quot schemes) and our new moduli of complete quotients. The topic on moduli of complete quotients is based upon a joint work with Baosen Wu.

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