Electrical discharge plasma formed in liquid water is under intensive investigation for many possible applications in biomedical, environmental and chemical engineering as well as for general scientific issues in plasma chemistry and other engineering applications. The subject of pulsed breakdown of water has additionally begun to assume importance due to growing interest in decontamination, purification of water containing chemical impurities and industrial sludge, and also in the emerging area of bio-electrics. This review paper focuses on the plasma physics (Part I) and chemistry of electrical discharges in liquid water and the chemical effects of plasmas on the degradation of organic molecules (Part II). This part discusses dielectric liquid breakdown and its mechanisms, streamer propagation and the effect of electrode polarity on streamer dynamics.