We describe modeling techniques from the field of Soft Computing (SC), and we illustrate their use in solving diagnostics and prognostics problems. Soft Computing is an association of computing methodologies that includes as its principal members fuzzy, neural, evolutionary, and probabilistic computing. These methodologies enable us to deal with imprecise, uncertain data and incomplete domain knowledge typically encountered in real-world applications. We analyze five successful SC case studies of applications to equipment diagnostics, forecasting, and control, e.g., prediction of voltage breakdown in power distribution networks, prediction of paper web breakage in paper mills, raw mix proportioning control in cement plants, diagnostics of power generation faults, and classification of MRI signatures for incipient failure detection. We conclude by projecting future trends of SC technologies and their use in constructing hybrid SC systems.