Nucleic-acid aptamers consisting in single-stranded DNA oligonucleotides emerged as very promising biorecognition elements for electrochemical biosensors applied in various fields such as medicine, environmental, and food safety. Despite their outstanding features, such as high-binding affinity for a broad range of targets, high stability, low cost and ease of modification, numerous challenges had to be overcome from the aptamer selection process on the design of functioning biosensing devices. Moreover, in the case of small molecules such as metabolites, toxins, drugs, etc., obtaining efficient binding aptamer sequences proved a challenging task given their small molecular surface and limited interactions between their functional groups and aptamer sequences. Thus, establishing consistent evaluation standards for aptamer affinity is crucial for the success of these aptamers in biosensing applications. In this context, this article will give an overview on the thermodynamic and structural aspects of the aptamer-target interaction, its specificity and selectivity, and will also highlight the current methods employed for determining the aptamer-binding affinity and the structural characterization of the aptamer-target complex. The critical aspects regarding the generation of aptamer-modified electrodes suitable for electrochemical sensing, such as appropriate bioreceptor immobilization strategy and experimental conditions which facilitate a convenient anchoring and stability of the aptamer, are also discussed. The review also summarizes some effective small molecule aptasensing platforms from the recent literature.