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In this paper, we survey some recent bounds on domination parameters. A characterisation of connected graphs with minimum degree at least 2 and domination number exceeding a third their size is obtained. Upper bounds on the total domination number, \(\gamma_t(G)\), of a graph \(G\) in terms of its order and size are established. If \(G\) is a connected graph of order \(n\) with minimum degree at least 2, then either \(\gamma_t(G) \leq 4n/7\) or \(G \in \{C_3,C_5,C_6,C_{10}\}\). A characterisation of those graphs of order \(n\) which are edge-minimal with respect to satisfying \(G\) connected, \(\delta(G) \geq 2\), and \(\gamma(G) \geq 4n/7\) is obtained. We establish that if \(G$ is a connected graph of size \(q\) with minimum degree at least 2, then \(\gamma_t(G) \leq (q + 2)/2\). Connected graphs \(G\) of size \(q\) with minimum degree at least 2 satisfying \(\gamma_t(G) > q/2\) are characterised. Upper bounds on other domination parameters, including the strong domination number and the restrained domination number are presented. We provide a constructive characterisation of those trees with equal domination and restrained domination numbers. A constructive characterisation of those trees with equal domination and weak domination numbers is also obtained.