Electrochemistry deals with the relation between electrical and chemical phenomena and has an ever-increasing impact on everybody's daily life. Out of the myriad applications of electrochemistry, considerable attention has been devoted to the fields of electrochemical (EC) sensing in recent decades because of its inherently fast, accurate, compact, portable, and cost-effective properties. In this scenario, the thesis work aims to address the challenges in the fields of EC sensing by using the rational design of nano-functional materials using graphene quantum dots (GQDs) and metal nanoclusters (MNC). The on-site monitoring of various analyte species in the environment by EC sensors requires enhanced sensitivity, specificity, and accuracy. Herein, we are trying to meet the aforementioned needs by developing various nano-functional materials based on GQDs and MNC. We have developed nitrogen (N-) and sulphur (S-) doped GQDs and gold (Au) and copper (Cu) -based NCs for the EC sensing of toxic heavy metal ions and biologically relevant molecules. The EC sensor materials exhibited excellent sensitivities and lowest detection limits reported hitherto, indicating the potentiality of the developed materials. In conclusion, this thesis presents an understanding of how the logical designing of nano-functional materials can meet the needs and conquer the challenges in the EC sensing of various analytes.