This dissertation considers the problem of estimation and inference in four high-dimensional models: (i) high-dimensional linear models, (ii) high-dimensional linear mixed effects models, (iii) high-dimensional varying coefficient models with functional random effects, and (iv) low-rank trace regression models. In the context of linear models, we propose procedures to construct asymptotic confidence intervals for low-dimensional parameters in the presence of high-dimensional nuisance covariates without the compatibility condition. Then, for linear mixed effects models, we consider a high-dimensional analogue of the Wald test for random effects, establishing its asymptotic distribution and power. In addition, we show that empirical Bayes estimation performs as well as the oracle asymptotically in estimating a part of the mean vector. Next, we consider a high-dimensional varying coefficient model with functional random effects. Under sampling times that are either fixed and common or random and independent, we propose a projection procedure to estimate and construct confidence bands for the varying coefficients. Finally, in low-rank trace regression, we establish an in-sample prediction error bound for the rank-constrained least-squares estimator and consider a permutation test for the entire matrix of regression coefficients.