The book gives an account of recent developments in the theory of nonparametric and semiparametric estimation. The first part deals with information lower bounds and differentiable functionals. The second part focuses on nonparametric maximum likelihood estimators for interval censoring and deconvolution. The distribution theory of these estimators is developed and new algorithms for computing them are introduced. The models apply frequently in biostatistics and epidemiology and although they have been used as a data-analytic tool for a long time, their properties have been largely unknown. Contents: Part I. Information Bounds: 1. Models, scores, and tangent spaces • 2. Convolution and asymptotic minimax theorems • 3. Van der Vaart's Differentiability Theorem • PART II. Nonparametric Maximum Likelihood Estimation: 1. The interval censoring problem • 2. The deconvolution problem • 3. Algorithms • 4. Consistency • 5. Distribution theory • References