It is now known that tropospheric thunderstorms and lightning discharges are electrodynamically coupled to the overlying upper atmospheric regions, ranging from the mesosphere to the lower ionosphere and extending to the radiation belts. In the mesosphere and the lower ionosphere this coupling leads to a fascinating menagerie of complex phenomena, including gigantic luminous displays (sprites), rapidly moving optical flashes (elves), and gamma ray flashes. The ELF/VLF electromagnetic impulses radiated by lightning discharges penetrate upward through the ionosphere into the radiation belts where they resonantly interact with the trapped energetic particle population. This process, known as lightning-induced electron precipitation (LEP) is believed to be an important determinant of the loss rates for energetic radiation belt electrons, which in turn is an important parameter for Space Weather, given the fact that high fluxes of such electrons are detrimental to spacecraft electronics. Lightning discharges occurring at cloud altitudes (<20 km) affect the upper atmosphere at altitudes >40 km either via the release of intense electromagnetic pulses (EMPs) and/or the production of intense quasi-static electric (QE) fields at mesospheric altitudes. Lightning involves rapid removal of charge built-up within the thundercloud. An average lightning discharge radiates an EMP of ~20 GW peak power, which propagates though the ionosphere and couples into the radiation belts, heating and ionizing the former and precipitating trapped energetic electrons from the latter. In addition, lightning discharges often produce intense transient QE fields of up to ~1 kV/m at 40--80 km altitudes, which for positive CG discharges is directed downwards, and which can thus avalanche accelerate upward-driven runaway MeV electron beams, producing brief (~1 ms) flashes of gamma radiation, both in the hemisphere of the parent lightning and in the conjugate hemisphere, and possibly contributing to the population of trapped radiation belt particles. Sprites are produced by the heating of ambient electrons in the mesosphere and lower ionosphere by the intense QE fields which temporarily (for a few to tens of milliseconds) exist at high altitudes following intense lightning flashes. The so-called 'Elves' are optical flashes which last much shorter (<1 ms) than sprites, and are typically limited to 80-95 km altitude, being produced by the heating, ionization, and optical emissions due to the electromagnetic impulses radiated by both positive and negative lightning discharges. We present a review of these phenomena, emphasizing the effects on Space Weather of tropospheric weather.