Aptamers are ligand-binding oligonucleotide sequences with high affinities and selectivities towards their targets. Concomitantly, their excellent recognition property has led to their being adapted in analytical applications, drug, diagnostics, and many other platforms in the area of forensic science, and in many respects, they are superior to analogous antibody-based assays. Recently, major progress has been made in biosensing applications of aptamers that offer the possibility of rapid and on-spot detection of seized drugs or illegal substances. Furthermore, aptamers may facilitate a future advancement in targeted delivery of anti-narcotics in the progression towards therapy. Hence, this review article provides an overview of electrochemical, optical, and colorimetric aptasensors developed so far and their potential future role in narcotics detection. We review advances made in aptamer sensing technology for cocaine, methamphetamine, codeine, and other opioid screening, and the potential obstacle at every stage of aptasensor development is also discussed. Finally, innovative concepts of using advanced nanomaterials and different sensing platforms are proposed for new generation aptasensor development for recreational drugs detection.