In countries where malaria transmission has decreased substantially, thanks to the scale-up of control interventions, malaria elimination may be feasible. Nevertheless, this goal requires new strategies such as the active detection and treatment of infected individuals. As the detection threshold for the currently used diagnostic methods is 100 parasites/μL, most low-density, asymptomatic infections able to maintain transmission cannot be detected. Identifying them by molecular methods such as PCR is a possible option but the field deployment of these tests is problematic. Isothermal amplification of nucleic acids (at a constant temperature) offers the opportunity of addressing some of the challenges related to the field deployment of molecular diagnostic methods. One of the novel isothermal amplification methods for which a substantial amount of work has been done is the loop-mediated isothermal amplification (LAMP) assay. The present review describes LAMP and several other isothermal nucleic acid amplification methods, such as thermophilic helicase-dependent amplification, strand displacement amplification, recombinase polymerase amplification and nucleic acid sequence-based amplification, and explores their potential use as high-throughput, field-based molecular tests for malaria diagnosis.