This paper provides an in-depth review of the optimal design of type-1 and type-2 fuzzy inference systems (FIS) using five well known computational frameworks: genetic-fuzzy systems (GFS), neuro-fuzzy systems (NFS), hierarchical fuzzy systems (HFS), evolving fuzzy systems (EFS), and multiobjective fuzzy systems (MFS), which is in view that some of them are linked to each other. The heuristic design of GFS uses evolutionary algorithms for optimizing both Mamdani-type and Takagi-Sugano-Kang-type fuzzy systems; whereas, the NFS combines the FIS with neural network learning method to improve the approximation ability. HFS combines two or more low-dimensional fuzzy logic units in a hierarchical design to overcome the curse of dimensionality. EFS solves the data streaming issues by refining (evolving) the system incrementally, and MFS solves the multi-objective trade-offs like the simultaneous maximization of both interpretability and accuracy. The overall synthesis of these dimensions explores the FIS's potential challenges and opportunities; the complex relations among the dimension; and the FIS's potential to combining one or more computational frameworks adding another dimension: deep fuzzy systems.