A hydrocarbon-based or ester-based drilling fluid or mud is described wherein the drilling fluid contains cesium phosphate. The hydrocarbon-based or ester-based drilling fluid or mud can have, for example, an external phase that contains hydrocarbon fluid and an internal phase that contains cesium phosphate. The hydrocarbon-based drilling fluid or mud can further contain at least one emulsifier or surfactant, and optionally other ingredients. The present invention can permit hydrocarbon-based drilling fluids to be essentially solids-free and may be used without corrosion and/or formation damage problems, for example, due to the use of the cesium phosphate in an internal phase of the hydrocarbon-based or ester-based drilling fluid. The present invention also relates to hydrocarbon-based or ester-based fluids for completion, workover, suspension and packer operations which contain cesium phosphate.