A search for the supersymmetric partners of the Standard Model bottom and top quarks is presented. The search uses 36.1 fbâ 1of pp collision data at s=13 TeV collected by the ATLAS experiment at the Large Hadron Collider. Direct production of pairs of bottom and top squarks (bÂ¯1and tÂ¯1) is searched for in final states with b-tagged jets and missing transverse momentum. Distinctive selections are defined with either no charged leptons (electrons or muons) in the final state, or one charged lepton. The zero-lepton selection targets models in which the bÂ¯1is the lightest squark and decays via bÂ¯1â bÏ Â¯10, where Ï Â¯10 is the lightest neutralino. The one-lepton final state targets models where bottom or top squarks are produced and can decay into multiple channels, bÂ¯1â bÏ Â¯10 and bÂ¯1â t or tÂ¯1â tÏ Â¯10 and tÂ¯1â b where Ï Â¯1Â± is the lightest chargino and the mass difference mÏ Â¯1Â±â mÏ Â¯10 is set to 1 GeV. No excess above the expected Standard Model background is observed. Exclusion limits at 95% confidence level on the mass of third-generation squarks are derived in various supersymmetry-inspired simplified models.