Memoryful Branching-Time Logic Traditional branching-time logics such as CTL* are memoryless: once a path in the computation tree is quantified at a given node, the computation that led to that node is forgotten. Recent work in planning suggests that CTL* cannot easily express temporal goals that refer to whole computations. Such goals require memoryful quantification of paths. With such a memoryful quantification, $E\psi$ holds at a node $s$ of a computation tree if there is a path $\pi$ starting at the root of the tree and going through $s$ such that $\pi$ satisfies the linear-time formula $\psi$. We define the memoryful branching-time logic mCTL* and study its expressive power and algorithmic properties. We show that mCTL* is as expressive, but exponentially more succinct, than CTL*, and that the ability of mCTL* to refer to the present is essential for this equivalence. From the algorithmic point of view, while the satisfiability problem for mCTL* is 2EXPTIME-complete --- not harder than that of CTL*, its model-checking problem is EXPSPACE-complete --- exponentially harder than that of CTL*. The upper bounds are obtained by extending the automata-theoretic approach to handle memoryful quantification, and are much more efficient than these obtained by translating mCTL* to branching logics with past. The EXPSPACE lower bound for the model-checking problem applies already to formulas of restricted form (in particular, to $AGE\psi$, which is useful for specifying possibility properties), and implies that reasoning about a memoryful branching-time logic is harder than reasoning about the linear-time logic of its path formulas.