We begin this section with a general overview
of the datasets that are available for PDF studies, before moving on
to discuss each process separately.
%
In Fig.~\ref{fig:kinplot-report} we show a
representative kinematical coverage in the
    $(x,Q^2)$ plane for the dataset included in a global
    analysis, in this case the recent NNPDF3.1 fit~\cite{nnpdf31}.
    %
 For the hadronic observables, leading order kinematics
    are assumed to map each data bin to a pair of $(x,Q^2)$
    values.
    %
    In Fig.~\ref{fig:kinplot-report}, the various datasets are clustered into families of
    related processes.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\begin{center}
  \includegraphics[scale=0.60]{3-datatheory/plots/kinplot-report.pdf}
  \caption{\small Typical kinematical coverage in the
    $(x,Q^2)$ plane for the dataset included in a global
    analysis, in this case NNPDF3.1.
    %
    For hadronic observables, leading order kinematics
    are assumed to map each data bin to a pair of $(x,Q^2)$
    values.
    %
    The various datasets are clustered into families of
    related processes.
    \label{fig:kinplot-report} 
  }
\end{center}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

We can see that a global dataset provides a rather wide coverage
in the $(x,Q^2)$ plane.
%
The low--$x$ and $Q^2$ region is dominated by the inclusive HERA structure function
measurements, which provide information down to $x\sim 3\cdot 10^{-5}$.
%
The high--$x$ region is covered by various processes, from fixed--target
DIS structure functions at low $Q^2$ to collider jet, Drell--Yan and top--quark
pair production at large $Q^2$.
%
The very high $Q^2$ region, up to a few ${\rm TeV}^2$, is only covered by inclusive jet production
data from ATLAS and CMS.
%
Until relatively recently, most PDF fits were based only on DIS and
fixed--target data, with some data from the Tevatron included. The breath of experimental
information that is now included in the latest PDF fits is therefore quite impressive, with data from processes such as the $Z$ $p_T$
and the $t\bar{t}$ differential distribution  only recently being considered for the first time.

In Table~\ref{tab:PDFsummarytable} we present another overview of the data entering a modern global PDF analysis. Here, we summarize
the various hard scattering processes which are used to constrain PDFs in a global analysis.
%
This table is an extended version of Table~1 of~\cite{Martin:2009iq}.
    %
 In each case we indicate the hadron--level process,
 the corresponding dominant 
 parton--level process, as well as the partons which
 are constrained in each case and the corresponding range of $x$.
 %
 Note that the latter are necessarily approximate, and only indicate in a qualitative
 way the $x$ region that dominates the PDF sensitivity of each measurement.
 %
 The necessity to include as broad a set of input datasets as possible, in order to constrain all quark flavour combinations and the gluon in the phenomenologically
 relevant region of $x$, is clear.
 %
 We also note that the medium--to--low-$x$ region, $x\lsim 0.01$, is mostly
 covered by the HERA collider structure functions as well as by some LHC data.
 %
 The very low--$x$ region, below the coverage of the HERA data,
 $x\lesssim 5\cdot 10^{-5}$, can only be accessed via $D$ meson production
 and exclusive $J/\psi$ production.
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{table}[h!]
\small
  \renewcommand{\arraystretch}{1.15}
  \begin{center}
    \begin{tabular}{lllll}
      \hline
      \hline
 &      Process & Subprocess & Partons & $x$ range \\ \hline
\multirow{7}{*}{Fixed Target}   &   $\ell^\pm\,\{p,n\}\to\ell^\pm+X$ & $\gamma^*q\to q$ & $q,\bar{q},g$ & $x\gtrsim 0.01$ \\
   &   $\ell^\pm\,n/p\to\ell^\pm+X$ & $\gamma^*\,d/u\to d/u$ & $d/u$ & $x\gtrsim 0.01$ \\
   &   $pp\to \mu^+\mu^-+X$ & $u\bar{u},d\bar{d}\to\gamma^*$ & $\bar{q}$ & $0.015\lesssim x\lesssim 0.35$ \\
   &   $pn/pp\to \mu^+\mu^-+X$ & $(u\bar{d})/(u\bar{u})\to \gamma^*$ & $\bar{d}/\bar{u}$ & $0.015\lesssim x\lesssim 0.35$ \\
   &   $\nu (\bar{\nu})\,N \to \mu^-(\mu^+)+X$ & $W^*q\to q^\prime$ & $q,\bar{q}$ & $0.01 \lesssim x \lesssim 0.5$ \\
   &   $\nu\,N \to \mu^-\mu^++X$ & $W^*s\to c$ & $s$ & $0.01\lesssim x\lesssim 0.2$ \\
   &   $\bar{\nu}\,N \to \mu^+\mu^-+X$ & $W^*\bar{s}\to\bar{c}$ & $\bar{s}$ & $0.01\lesssim x\lesssim 0.2$ \\
   \hline
\multirow{5}{*}{Collider DIS}   &   $e^\pm\,p \to e^\pm+X$ & $\gamma^*q\to q$ & $g,q,\bar{q}$ & $0.0001\lesssim x\lesssim 0.1$ \\
   &   $e^+\,p \to \bar{\nu}+X$ & $W^+\,\{d,s\}\to \{u,c\}$ & $d,s$ & $x\gtrsim 0.01$ \\
   &   $e^\pm p\to e^\pm\,c\bar{c}+X$ & $\gamma^*c\to c$, $\gamma^* g\to c\bar{c}$ & $c$, $g$ & $10^{-4}\lesssim x\lesssim 0.01$ \\
   &    $e^\pm p\to e^\pm\,b\bar{b}+X$ & $\gamma^*b\to b$, $\gamma^* g\to b\bar{b}$ & $b$, $g$ & $10^{-4}\lesssim x\lesssim 0.01$ \\	
   &   $e^\pm p\to\text{jet}+X$ & $\gamma^*g\to q\bar{q}$ & $g$ & $0.01\lesssim x\lesssim 0.1$ \\
   \hline
\multirow{4}{*}{Tevatron}    &   $p\bar{p}\to \text{jet}+X$ & $gg,qg,qq\to 2j$ & $g,q$ & $0.01\lesssim x\lesssim 0.5$ \\
   &   $p\bar{p}\to (W^\pm\to\ell^{\pm}\nu)+X$ & $ud\to W^+,\bar{u}\bar{d}\to W^-$ & $u,d,\bar{u},\bar{d}$ & $x\gtrsim 0.05$ \\
   &   $p\bar{p}\to (Z\to\ell^+\ell^-)+X$ & $uu,dd\to Z$ & $u,d$ & $x\gtrsim 0.05$ \\
   &   $p\bar{p} \to t\bar{t}+X$ & $qq\to t\overline{t}$& $q$ & $x \gtrsim 0.1$ \\
       \hline
\multirow{11}{*}{LHC}    &   $pp\to \text{jet}+X$ & $gg,qg,q\bar{q}\to 2j$ & $g,q$ & $0.001\lesssim x\lesssim 0.5$ \\
   &   $pp\to (W^\pm\to\ell^{\pm}\nu)+X$ & $u\bar{d}\to W^+,d\bar{u}\to W^-$ & $u,d,\bar{u},\bar{d},g$ & $x\gtrsim 10^{-3}$ \\
   &   $pp\to (Z\to\ell^+\ell^-)+X$ & $q\bar{q}\to Z$ & $q,\bar{q},g$ & $x\gtrsim 10^{-3}$ \\ 
   &   $pp\to (Z\to\ell^+\ell^-)+X$, $p_\perp$ & $gq(\bar{q})\to Z q(\bar{q})$ & $g,q,\bar{q}$ & $x\gtrsim 0.01$ \\ 
   &   $pp\to (\gamma^*\to\ell^+\ell^-)+X$, Low mass & $q\bar{q}\to \gamma^*$ & $q,\bar{q},g$ & $x\gtrsim 10^{-4}$ \\
   &    $pp\to (\gamma^*\to\ell^+\ell^-)+X$, High mass & $q\bar{q}\to \gamma^*$ & $\bar{q}$ & $x\gtrsim 0.1$ \\	
   &    $pp\to W^+ \bar{c}, W^- c$ & $sg \to W^+ c$, $\bar{s}g\to W^- \bar{c}$ & $s,\bar{s}$ & $x\sim 0.01$\\
   &    $pp \to t\bar{t}+X$ & $gg\to t\overline{t}$& $g$ & $x\gtrsim 0.01$ \\
   &    $pp \to D,B+X$ & $gg\to c\bar{c},$ $b\bar{b}$& $g$ & $x \gtrsim 10^{-6},10^{-5}$ \\
   &    $pp \to J/\psi, \Upsilon+ pp$ & $\gamma^*(gg)\to c\bar{c},$ $b\bar{b}$& $g$ & $x \gtrsim 10^{-6},10^{-5}$ \\
   &    $pp \to \gamma+ X$ & $g q(\bar{q}) \to \gamma q(\bar{q})$& $g$ & $x \gtrsim 0.005$ \\
       \hline
    \end{tabular}
  \end{center}
  \caption{Overview of the various hard-scattering processes which are used to constrain PDFs in a global analysis. In each case we indicate the hadronic-level process and the corresponding dominant partonic level process, as well as the partons which are constrained by each specific process in a given range of $x$. This table
  is an extended version of Table 1 of~\cite{Martin:2009iq}.
  %
  The $x$ ranges are merely indicative and based on the approximate leading-order kinematics.
  }
  \label{tab:PDFsummarytable}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

In the rest of this section, we discuss one by one
the various processes that can be used to constrain the parton distributions
in a global analysis, listed in Table~\ref{tab:PDFsummarytable}.
%
We follow the same structure for each process: first of all we review the PDF sensitivity,
then we discuss the available measurements,
followed by a description of the state-of-the-art of the corresponding theoretical calculations, to conclude with some
representative illustrations of the impact of each family of processes in the PDF fit.

In the following, we restrict the discussion to theoretical calculations based on fixed--order perturbative
QCD; see Refs.~\cite{White:2006yh,Bonvini:2017ogt} and~\cite{Bonvini:2015ira} for
studies of the impact of the PDF fit of theory calculations based
on all-order resummations of logarithmically enhanced terms at small-$x$ and large-$x$
respectively.
