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We have investigated intersubband transitions (ISBTs) in InAs/AlSb multiple quantum wells. In wells from 7 to 10 nm wide, the ISBT energy increases with decreasing well width and temperature. We do not observe photoluminescence (PL) from these wells. In wells from 2.4 to 6 nm wide, we observe PL but not ISBTs. We have calculated the band structure of these samples using an 8 band k.p theory including strain and many-body effects. We have modelled the dependence of the ISBT energy on well width and temperature. In addition, we have observed the effects on ISBTs of QW interface type and Si doping in the well.