  We study semiresolutions of quasi-projective varieties with properties $G_1$,
$S_2$, and seminormality. Equivalently, these are varieties $X$ with Serre's
$S_2$ property, such that there exists an open subvariety $U$, with complement
of codimension at least two, such that the only singularities of $U$ are
(analytically) double normal crossings. Such varieties have been called
"demi-normal" by Koll\'ar \cite{Kol13}. First, we discuss why these properties
are ideal for the study of nonnormal varieties that appear in the birational
classification of varieties. We define semiresolutions and provide examples to
illustrate the procedure of gluing along the conductor as the fundamental tool
in obtaining a semiresolution of $X$ from a resolution of its normalization. As
an application of these methods, we discuss semirational singularities. Our
main results are a semismooth Grauert-Riemenschneider vanishing theorem
(Theorem 4.2) and a proof that the definition of semirational singularities
does not depend on the semiresolution chosen (Theorem 4.3) . The smooth version
of (4.2) first appeared in \cite{GR70}. We also explain why semirational
singularities are, in particular, Cohen-Macaulay and DuBois. Finally, we
discuss the role semiresolutions play in forming a nonnormal interpretation of
the results of de Fernex and Hacon in \cite{dFH09}, where the
$\mathbb{Q}$-Cartier hypothesis was found to be extraneous in the birational
classification of normal varieties.
