The paper examines the prospects of using laser plasmas for studying novel regimes ofthe magnetic field line reconnection and charged particle acceleration. Basic features ofplasma dynamics in the three-dimensional configurations relevant to the formation of currentsheets in a plasma are addressed by analyzing exact self-similar solutions of the magnetohydrodynamicsand electron magneto-hydrodynamics equations. Then the magnetic fieldannihilation in the ultrarelativistic limit is considered, when the opposite polarity magneticfield is generated in collisionless plasma by multiple laser pulses, in the regime with adominant contribution of the displacement current exciting a strong large-scale electricfield. This field leads to the conversion of the magnetic energy into the kinetic energy ofaccelerated particles inside a thin current sheet. Charged particle acceleration during magneticfield reconnection is discussed when radiation friction and quantum electrodynamics effectsbecome dominant.