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The book is concerned with two types of microstructure fluids namely, micropolar fluids and microstretch fluids. It also includes an application of micropolar fluid subject to a magnetic field or an electric field. In chapter 1, the field and constitutive equations of microstretch and micropolar fluids are presented. The constitutive equations as developed by Eringen are also presented in tensor and dyadic forms. Different boundary condition for the velocity, microrotation and the microstretch are investigated. In chapter 2, the problem of an isothermal, incompressible magneto - micropolar hydrodynamic fluid in an infinitely magnetic insulating circular cylinder is considered. The fluid is under a constant magnetic field perpendicular to the axis of the cylinder. The fluid properties are considered to be constant. The slip boundary conditions for velocity and microrotation are applied. Closed forms for the velocity, microrotation and magnetic field are obtained for Poiseuille and Couette flows. Expressions for the rate of flow and skin coefficients are calculated. Variations of the physical quantities with respect to micropolarity parameter, slip parameters.