Beta regression models are becoming popular in diverse fields of application because these models simultaneously model mean and variance for a variety of data. Optimal designs for these models have got little attention in literature. In this study we focus on the construction of optimal designs for fitting single and multi-response beta regression models for unrestricted and restricted design regions assuming the mean-precision parameterization of beta distribution. The optimality criteria in focus for single response models are the D- and the Ds-criterion, whereas for multi-response models the focus is D- and generalized D-criteria. Considering the form of beta regression model proposed by Ferrari and Cribari-Neto (2004), D-optimal designs are constructed for models involving one and two predictors. A visual approach to guess the locations of design points from mean function plot is suggested and applied. The robustness of constructed designs to parameter misspecification is also addressed. Optimal designs vary both in terms of number and locations of design points and are not always balanced. Ds-optimal designs for precise estimation of parameters of mean sub-model are found to be balanced saturated designs making visual assessment of the design structure easier. The structure of D-optimal designs constructed for models with two predictors varies in consonance with parameter spaces of the respective models. Contrary to single predictor models, use of the Ds-criterion for design construction does not simplify the design structure. Exploiting the general class of beta regression models of Simas et al. (2010), optimal designs are developed for models with one and two predictors. The visual approach is eloquently extended to models with single predictor for assessment of the design structure using plots of mean and precision parameters. Optimal designs for models with single predictor are compared with various standard designs to identify alternative efficient designs. The constructed designs for models with two predictors are compared with equiweighted designs including a two-factor factorial design and a few variants in search for alternatives to optimal designs for practical use. As locally optimal designs are not robust, sequentially constructed designs are presented for single predictor models as their alternative. These designs prove to be efficient regardless of the severity level of parameter misspecification and the size of the experiment. Individually Optimal Design (IOD) and Jointly Optimal Design (JOD) for multi-response beta regression models with single predictor as defined by Souza and Moura (2012a) are studied. The knowledge of shapes of mean functions and information about the structure of IODs is found to be useful in assessing the structure of JODs. When responses are independent D-optimal designs are explored for two- and three-response models. A strategy for using the generalized D-criterion to construct optimal designs for multi-response generalized linear models is suggested and is applied to construct JODs for kresponse beta regression models. Robustness of JODs with respect to varying multi-response models is examined. IODs and JODs are compared with each other and performance of standard designs relative to JODs is also evaluated. Applications of the designs constructed for models under study to real-life problems are given for each class of models.