Microfluidic　droplet　technology　has　been　developing　rapidly.　However,　precise　control　of　dynamical　behaviour　of　droplets　remains　a　major　hurdle　for　new　designs.　This　study　is　to　understand　droplet　deformation　and　breakup　under　simple　shear　flow　in　confined　environment　as　typically　found　in　microfluidic　applications.　In　addition　to　the　Newtonian-Newtonian　system,　we　consider　also　both　a　Newtonian　droplet　in　a　non-Newtonian　matrix　fluid　and　a　non-Newtonian　droplet　in　a　Newtonian　matrix.　The　lattice　Boltzmann　method　is　adopted　to　systematically　investigate　droplet　deformation　and　breakup　under　a　broad　range　of　capillary　numbers,　viscosity　ratios　of　the　fluids,　and　confinement　ratios　considering　shear-thinning　and　shear-thickening　fluids.　Confinement　is　found　to　enhance　deformation,　and　the　maximum　deformation　occurs　at　the　viscosity　ratio　of　unity.　The　droplet　orients　more　towards　the　flow　direction　with　increasing　viscosity　ratio　or　confinement　ratio.　In　addition,　it　is　noticed　that　the　wall　effect　becomes　more　significant　for　confinement　ratios　larger　than　0.4.　Finally,　for　the　whole　range　of　Newtonian　carrier　fluids　tested,　the　critical　capillary　number　above　which　droplet　breakup　occurs　is　only　slightly　affected　by　the　confinement　ratio　for　a　viscosity　ratio　of　unity.　Upon　increasing　the　confinement　ratio,　the　critical　capillary　number　increases　for　the　viscosity　ratios　less　than　unity,　but　decreases　for　the　viscosity　ratios　more　than　unity.