In this review, the classification of magnetoresistance effects, the electrical conduction mechanisms without and with magnetic field, and the spintronics are briefly summarized. The magnetoresistance effect in the molecular systems including small organic molecules, carbon nanotubes, graphene, conductive polymers and their nanocomposites is critically reviewed. The four normally used models are elaborated to disclose the mechanisms of organic magnetoresistance (OMAR) in the organic systems. The most current applications of these molecular systems are also summarized. These molecular systems are envisioned to create next-generation spintronic and electronic devices for flexible applications.