Natural organic matter (NOM) is ubiquitous in the aquatic environment and if present can cause varied drinking water quality issues, the major one being disinfection byproduct (DBP) formation. Trihalomethanes (THMs) are major classes of DBP that are formed during chlorination of NOM. The best way to remove DBPs is to target the precursors (NOM) directly. The main aim of this review is to study conventional as well as advanced ways of treating NOM, with a broad focus on NOM removal using advanced oxidation processes (AOPs) and biofiltration. The first part of the paper focuses on THM formation and removal using conventional processes and the second part focuses on the studies carried out during the years 2000–2018, specifically on NOM removal using AOPs and AOP-biofiltration. Considering the proven carcinogenic nature of THMs and their diverse health effects, it becomes important for any drinking water treatment industry to ameliorate the current water treatment practices and focus on techniques like AOP or synergy of AOP-biofiltration which showed up to 50–60% NOM reduction. The use of AOP alone provides a cost barrier which can be compensated by the use of biofiltration along with AOP with low energy inputs, making it a techno-economically feasible option for NOM removal.