  The main purpose of this article is to survey on some key elements of a
recent $\mathcal{H}_p$-theory of general Dirichlet series $\sum a_n
e^{-\lambda_{n}s}$, which was mainly inspired by the work of Bayart and Helson
on ordinary Dirichlet series $\sum a_n n^{-s}$. In view of an ingenious
identification of Bohr, the $\mathcal{H}_p$-theory of ordinary Dirichlet series
can be seen as a sub-theory of Fourier analysis on the infinite dimensional
torus $\mathbb{T}^\infty$. Extending these ideas, the $\mathcal{H}_p$-theory of
$\lambda$-Dirichlet series is build as a sub-theory of Fourier analysis on what
we call $\lambda$-Dirichlet groups. A number of problems is added.
