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This paper discusses three issues related to lightning. The first is to provide a quantitative physical explanation of the lightning stepped leader, whereby breakdown from a cloud to the ground proceeds by luminous steps about 50 m in length, with about 50 μs separating each step. The second is to explain the initiation of upward leaders from tall objects on the ground, induced by the downward leaders from the cloud. Of particular importance is the concept of "critical radius," used in calculations for the effective attractive radius for the collection of lightning by lightning rods. The third, is the unresolved issue of "ball lightning," where observations have been reported during thunderstorms of luminous spheres of plasma a few centimeters in diameter, moving about 1 m above the ground for periods of up to 10 s, existing inside houses and even aeroplanes. Approximate quantitative calculations are given as proposed explanations of these phenomena, using numerical calculations based on the continuity equations for electrons and ions and also Poisson's Equation to account for space charge effects. Also used are the two material properties of air that at 1 bar the electric field to initiate breakdown is 2.5 MV/m (25 kV/cm) and the field required to sustain a glow discharge is 0.5 MV/m (5 kV/cm).