This work summarizes some of our recent theoretical studies on convective heat transfer in micro-geometries. Only pure analytical solutions are presented here. At first, forced convection is studied for the following three geometries: microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant heat flux is assumed to be applied at walls. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. In the analysis, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. In the forced convection problems, viscous dissipation is also included, while it is neglected for the mixed convection problem. Internal velocity and temperature distributions are obtained for varying values of governing parameters. Finally, fully analytical Nusselt number correlations are developed for the cases investigated.