When the flying height is below 5 nm, some physical phenomena that can be ignored for higher flying sliders need to be included in the modeling equations. Another challenging issue is the unavoidable asperity contact problem. It is known that zero spacing at asperities may cause some of the existing modified Reynolds equations to predict unphysical unbounded contact pressure singularities. In this paper we first review the source of these pressure singularities, showing which models have this problem and which do not. We also review here a new derivation of a compressible lubrication equation by using a different slip velocity boundary condition, in which additional slippage at the gas-solid interface due to pressure gradient is introduced. The new equation is free of any contact singularity . Next we review our recent work on the non-negligible effect of the intermolecular forces on the slider’s flying attitude when the spacing is below 5 nm . The additional force is attractive until the spacing is below about 0.1 nm for example and then it is repulsive. Finally we show the effect of these new force contributions on the flying attitude of a low flying slider.