In this article, we consider isolated cliques and isolated dense subgraphs. For a given graph G, a vertex subset S of size k (and also its induced subgraph G(S)) is said to be c-isolated if G(S) is connected to its outside via less than ck edges. The number c is sometimes called the isolation factor. The subgraph appears more isolated if the isolation factor is smaller. The main result in this work shows that for a fixed constant c, we can enumerate all c-isolated maximal cliques (including a maximum one, if any) in linear time.In more detail, we show that, for a given graph G of n vertices and m edges, and a positive real number c, all c-isolated maximal cliques can be enumerated in time O(c 4 2 2c m). From this, we can see that: (1) if c is a constant, all c-isolated maximal cliques can be enumerated in linear time, and (2) if c = O(log n), all c-isolated maximal cliques can be enumerated in polynomial time. Moreover, we show that these bounds are tight. That is, if f (n) is an increasing function not bounded by any constant, then there is a graph of n vertices and m edges for which the number of f (n)-isolated maximal cliques is superlinear in n + m. Furthermore, if f (n) = ω(log n), there is a graph of n vertices and m edges for which the number of f (n)-isolated maximal cliques is superpolynomial in n + m.We next introduce the idea of pseudo-cliques. A pseudo-clique having an average degree α and a minimum degree β, denoted by PC(α, β), is a set V ⊆ V such that the subgraph induced by V has an average degree of at least α and a minimum degree of at least β. This article investigates these, and obtains some cases that can be solved in polynomial time and some other cases that have a superpolynomial number of solutions. Especially, we show the following results, where k is the number of vertices of the isolated pseudo-cliques: (1) For any ε > 0 there is a graph of n vertices for which the number of 1-isolated PC(k − (log k) 1+ε , k (log k) 1+ε ) is superpolynomial, and (2) there is a polynomial-time algorithm which enumerates all c-isolated PC(k − log k, k log k ), for any constant c.