Let $X$ be a simple, simply connected algebraic group over an algebraically closed field $k$ of characteristic $p$.
Steinberg's tensor product theorem states that if $V$ is a finite dimensional irreducible $kX$-module then $V$ = $V_1 ^{(q_1)} \otimes \ldots \otimes V_n ^{(q_n)}$ where each $V_i$ is a restricted $kX$-module and the $q_i$ are distinct powers of $p$.
This theorem can be reformulated in terms of rational representations instead of modules as follows: any irreducible rational representation $\Phi : X \rightarrow SL(V)$ can be factorised as $\Phi : X \xrightarrow{\text{$\Psi$}} X \times X \times \ldots \times X \xrightarrow{\text{$\mu$}} SL(V)$ with $\Psi : x \rightarrow (x^{(q_1)} , \ldots , x^{(q_j)})$ where $x^{(q_i)}$ denotes the image of $x$ under the standard Frobenius $q_i$ map and $\mu$ restricts to a completely reducible restricted representation on each factor.
Liebeck and Seitz proved a generalisation of this theorem where the target group $SL(V)$ is replaced by an arbitrary simple algebraic group $G$ over $k$ in good characteristic.
A consequence of this theorem is that every connected simple $G$-completely reducible ($G$-cr) subgroup $X$ of $G$ is contained in a uniquely determined commuting product $R_1 \ldots R_n$ in $G$ such that each $R_i$ is a simple restricted subgroup of the same type as $X$ and each projection $X \rightarrow R_i / Z(R_i)$ is non trivial and involves a different field twist.
Here saying that $X$ is $G$-cr means that whenever $X$ is contained in a parabolic subgroup $P$ of $G$, it is contained in a Levi subgroup of $P$.
The first new theorem of this thesis is a converse of this result: if $G$ is of exceptional type in good characteristic and $X$ is contained in such a product $R_1 \ldots R_n$, then $X$ is $G$-cr, with two exceptions.
If $G$ is of classical type we prove a similar theorem with the extra assumption that the $R_i$ are $G$-cr.

In view of these results, it is of interest to determine the products $R_1 \ldots R_n$ of more than one restricted subgroup of the same type in exceptional algebraic groups; this is achieved in the rest of this thesis.

The above results have a number of consequences.
First, every restricted connected simple subgroup of $G$ is $G$-cr with two exceptions.
We also classify all non-restricted $G$-cr simple subgroups of exceptional groups.
We find the centralisers of all products of more than one subgroup of the same type and of all non-restricted $G$-cr simple subgroups.
We also prove that the conjugacy classes of such subgroups are uniquely determined by the restriction of the Lie algebra of $G$.