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The objective of this work is to study the effects of charge redistribution, applied layer-normal electric fields, applied strain, and layer engineering on the band alignment of Black Phosphorus (BP)/Molybdenum disulphide (MoS2) heterostructure through Density Functional Theory (DFT) simulations. Black phosphorus works as a p-type material with high mobility, mechanical flexibility, and sensitivity to number of layers. Combining it with the more electronegative material, MoS2 results in strong carrier confinement and a Type II heterostructure. Charge redistribution among the layers shifts the band alignment expected from the Electron Affinity Rule. Applied external fields, strain and multiple BP layers provide band-alignment tunability within the Type II range and/or, transition to Type I and Type III heterostructures. The tunability in BP/MoS2 heterostructure may be useful as tunnel field effect transistors, rectifier diodes with tunable barrier height, reconfigurable FETs, and electro-optical modulators. Furthermore, considering heterostructures of monolayer BP with other monolayer Transitional Metal Dichalcogenides (TMD) suggests the ability to achieve different band alignment types. In our simulations, a Type I alignment is found with Tungsten diselenide (WSe2), Molybdenum diselenide (MoSe2), and Tungsten disulphide (WS2), and a Type III for Hafnium disulphide (HfS2) and Hafnium diselenide (HfSe2).