Nowadays, the energy consumption and the heat dissipation of computing environments have emerged as crucial issues. Indeed, large data centers consume as much electricity as a city while modern processors attain high temperatures degrading their performance and decreasing their reliability. In this thesis, we study various energy and temperature aware scheduling problems and we focus on their complexity and approximability. A dominant technique for saving energy is by proper scheduling of the jobs through the operating system combined with appropriate scaling of the processor’s speed. This technique is referred to as speed scaling in the literature. The theoretical study of speed scaling was initiated by Yao, Demers and Shenker (1995) who considered the single-processor problem of scheduling preemptively a set of jobs, each one specified by an amount of work, a release date and a deadline, so as to minimize the total energy consumption. In order to measure the energy consumption of a processor, the authors considered the well-known rule according to which the processor’s power consumption is P(t) = s(t)α at each time t, where s(t) is the processor’s speed at t and α > 1 is a machine-dependent constant (usually α ∈ [2, 3]). Here, we study speed scaling problems on a single processor, on homogeneous parallel processors, on heterogeneous environments and on shop environments. In most cases, the objective is the minimization of the energy but we also address problems in which we are interested in capturing the trade-off between energy and performance. We tackle speed scaling problems through different approaches. For non-preemptive problems, we explore the idea of transforming optimal preemptive schedules to nonpreemptive ones. Moreover, we exploit the fact that some problems can be formulated as convex programs and we propose greedy algorithms that produce optimal solutions satisfying the KKT conditions which are necessary and sufficient for optimality in convex programming. In the context of convex programming and KKT conditions, we also study the design of primal-dual algorithms. Additionally, we solve speed scaling problems by formulating them as convex cost flow or minimum weighted bipartite matching problems. Finally, we elaborate on approximating energy minimization problems that can be formulated as integer configuration linear programs. We can obtain an approximate solution for such a problem by solving the fractional relaxation of an integer configuration linear program for it and applying randomized rounding. In this thesis, we solve some new energy aware scheduling problems and we improve the best-known algorithms for some other problems. For instance, we improve the bestknown approximation algorithm for the single-processor non-preemptive energy minimization problem which is strongly NP-hard. When α = 3, we decrease the approximation ratio from 2048 to 20. Furthermore, we propose a faster optimal combinatorial algorithm vii viii for the preemptive migratory energy minimization problem on power-homogeneous processors, while the best-known algorithm was based on solving linear programs. Last but not least, we improve the best-known approximation algorithm for the preemptive nonmigratory energy minimization problem on power-homogeneous processors for fractional values of α. Our algorithm can be applied even in the more general case where the processors are heterogeneous and, for αmax = 2.5 (which is the maximum constant α among all processors), we get an improvement of the approximation ratio from 5 to 3.08. In order to manage the thermal behavior of a computing device, we adopt the approach of Chrobak, Dürr, Hurand and Robert (2011). The main assumption is that some jobs are more CPU intensive than others and more heat is generated during their execution. So, each job is associated with a heat contribution which is the impact of the job on the processor’s temperature. In this setting, we study the complexity and the approximability of multiprocessor scheduling problems where either there is a constraint on the processors’ temperature and our aim is to optimize some performance metric or the temperature is the optimization goal itself.