In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, $f$-max quasi-independent set, consists of, given a graph and a non-decreasing function $f$, finding a maximum size subset $Q$ of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to $f(\vert Q \vert)$. For this problem, we show an exact solution method that runs within time $O^\ast(2^{\frac{d-27/23}{d+1}n})$ on graphs of average degree bounded by $d$. For the most specifically defined $\gamma$-max quasi-independent set and $k$-max quasi-independent set problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.