We have performed a detailed HI study of the Magellanic Stream (MS). Using the LAB all-sky HI survey, we expose the MS to be composed of two filaments distinct both spatially (as first pointed out by Putman et al. 2003) and in velocity. One of the MS filaments and parts of the Leading Arm (LA) can be traced back to their origin in the SouthEast HI Overdensity (SEHO) of the LMC, which includes 30 Doradus. Therefore, at least one-half of the trailing Stream and most of the LA originates in the LMC, contrary to previous assertions that they originate in the SMC and/or in the Magellanic Bridge. The two MS filaments show periodic spatial and velocity patterns that we speculate are an imprint of the LMC rotation curve. If true, then the drift rate of the Stream gas away from the Magellanic Clouds is ∼49 km s −1 and the age of the MS is ∼1.74 Gyr. High-resolution HI data of the LMC show gas outflows from supergiant shells in the SEHO that seem to be creating the LA and LMC filament of the MS. We lay out a new model, the "Blowout Hypothesis", for the formation of the MS that fits all of the available data and solves some longstanding problems. We also conducted a ∼200 deg 2 HI survey with the GBT at the tip of the MS in order to bridge the gap between the ∼100 ◦ –long "classical" MS and the MS–like emission reported by Braun & Thilker (2004). Our survey shows that the MS gas is continuous across the gap and that the MS is at least ∼140 ◦ long. A previously unknown velocity inflection in the MS-tip is also revealed in the data. The mass of the newly-found ∼40 ◦ extension of the MS–tip is ∼5×10 7 M ⊙ which increases the total mass of the MS by ∼10%. We estimate that the age of the ∼140 ◦ –long MS is ∼2.5 Gyr which coincides with bursts of star formation in the Magellanic Clouds and a possible close encounter of these two galaxies with each other. These new observational characteristics of the MS offer additional new constraints on MS simulations. Note: Abstract extracted from PDF text