This work addresses the algorithmic tractability of hard combinatorial problems. Basically, we are considering \NP-hard problems. For those problemsrnwerncan not find a polynomial time algorithm. Several algorithmic approaches already exist which deal with this dilemma. Amongrnthemrnwe find (randomized) approximation algorithms and heuristics. Even though in practice they often work in reasonable time they usually do not return anrnoptimal solution. If we constrain optimality then there are only two methods which suffice for this purpose: exponential time algorithms andrnparameterized algorithms. In the first approach we seek to design algorithms consuming exponentially many steps who are more clever than some trivialrnalgorithm (whornsimply enumerates all solution candidates).rnTypically, the naive enumerative approach yields an algorithm with run time $\Oh^*(2^n)$. So, the general task is to construct algorithms obeying a run time of rnthe form $\Oh^*(c^n)$ where $c<2$.rn The second approach considers an additional parameter $k$ besides the input size $n$. This parameter shouldrnprovide more information about the problem and cover a typical characteristic. The standard parameterization is to see $k$ as an upper (lower, resp.)rnbound on the solution size in case of a minimization (maximization, resp.) problem. Then a parameterized algorithm should solve the problem in time $f(k)\cdot n^\beta$rnwhere $\beta$ is a constant and $f$ is independent of $n$. In principle this method aims to restrict the combinatorial difficulty of the problem tornthe parameter $k$ (if possible). The basic hypothesis is that $k$ is small with respect to the overall input size.rnIn both fields a frequent standard technique is the design of branching algorithms. These algorithms solve the problem by traversing the solutionrnspace in a clever way. They frequently select an entity of the input and create two new subproblems, one where this entity is considered as part ofrnthernfuture solution and another one where it is excluded from it. Then in both cases by fixing this entity possibly other entities will be fixed. If so then therntraversedrnnumber of possible solution is smaller than the whole solution space. The visited solutions can be arranged like a search tree. To estimate thernrun time of such algorithms there is need for a method to obtain tight upper bounds on the size of the search trees. In the field of exponential timernalgorithms a powerful technique called Measure&Conquer has been developed for this purpose. It has been applied successfully to manyrnproblems, especially to problems where other algorithmic attacks could not break the trivial run time upper bound. rnOn the other hand in the field of parameterized algorithms Measure&Conquer is almost not known. This piece of work will presentrnexamples where this technique can be used in this field. It also will point out what differences have to be made in order to successfully applyrnthe technique. Further, exponential time algorithms for hard problems where Measure&Conquer is applied are presented. Another aspect is thatrna formalization (and generalization) of the notion of a search tree is given. It is shown that for certain problems such a formalization is extremely useful.rn