  This survey mainly deals with the tilted Carath{\'e}odory class by angle
$\lambda$ (denoted by $\mathcal{P}_{\lambda}$) an element of which maps the
unit disc into the tilted right half-plane $\{w: \Re e^{i\lambda} w>0\}$.
Firstly we will characterize $\mathcal{P}_{\lambda}$ from different aspects. In
section 3, various estimates of functionals over $\mathcal{P}_{\lambda}$ are
deduced from the known corresponding estimates of $\mathcal{P}_{0}$ or
elementary functional analysis. Finally some subsets of analytic functions
related to $\mathcal{P}_{\lambda}$ including close-to-convex functions with
argument $\lambda$, $\lambda$-spirallike functions, $\lambda$-Robertson
functions and analytic functions whose derivative is in $\mathcal{P}_{\lambda}$
are also considered as applications
