This paper considers semi-nonparametric conditional moment models where the parameters of interest include both finite-dimensional parameters and unknown functions. We mainly focus on two inferential problems in this framework. First, we provide new methods of uniform inference for the estimates of both finite- and infinite-dimensional components of the parameters and functionals of the parameters. Based on these results, we can, for instance, construct uniform confidence bands for the unknown functions and the partial derivatives of the unknown functions. Recently, uniform confidence bands for a variety of models such as conditional mean and quantiles have been introduced using strong approximation methods. We provide uniform inference in conditional moment restriction models with endogeneity. Second, for a large class of conditional moment restrictions models, we provide new results for inference when parameters are only partially identified. Under partial identification, we show how to construct pointwise confidence regions by inverting a quasi-likelihood ratio (QLR) statistic that is also employed under point identification. We provide a consistent multiplier bootstrap procedure for obtaining critical values corresponding to the QLR. Furthermore, we generalize the uniform confidence bands from point identified case to uniform confidence sets over the domain of the unknown functions by inverting a sup-QLR statistic. The new methods are applied to construct pointwise confidence intervals and uniform confidence bands for shape-invariant Engel curves.