The article provides the definition of the essence of derivative financial instruments (derivatives); identifies possible scenarios for their use based on hedging (insuring risks against possible losses), speculation (making deals for profit), arbitration (fixed income from making deals for one asset, which are opposite to each other). The authors carry out an analysis of the current state of the derivatives market in Russia and determine the dynamics of trading volumes on the derivatives market in 2015-2017. The authors also identify the problems of the derivatives market: the inability to fully use cross-border relations, the lack of guarantees for the parties to fulfill their obligations to the full, biased resolution of disputes by interested parties, imbalance in the system for regulating derivatives; The article provides some possible solutions to the problems in the derivatives market: the increased transparency of transactions, protection of investors' interests, integration of financial markets, emergence of global regulatory bodies, whose implementation will improve the position in the derivatives market. The authors also specify the types of derivative financial instruments.