Populations often experience environmental conditions that are variable both in space and in time. Understanding the demographic and evolutionary dynamics of populations in such variable environments has very practical implications for conservation biology, pest and pathogen control, management of antibiotic resistance. This thesis is an attempt to study the ecological and evolutionary implications of spatial and temporal variations of the environment.First, I study how spatially heterogeneous and temporally changing conditions influence the demographic dynamics of a genetically uniform population. The growth of the population is enhanced when individuals preferentially accumulate in high quality habitats. Migration between locations facilitates a good arrangement of individuals such that in general, an intermediate rate of migration maximizes the growth rate.Second, I develop a model where the growth rate of individuals depends on the environment but also on their genetic quality, and possibly on the interaction between the environment and the genotype. If the performance of different genotypes tradeoffs across the environments, several genotypes may be maintained locally in the environment that suit them and a pattern of local adaptation emerges. Moreover, I show that adaptation of populations to environmental fluctuations in the environment generates very dynamic changes in the genetic composition that lag behind the environmental change. Adaptation may be facilitated by the influx of migrants coming from other demes.How can we detect such patterns of adaptation in wild or experimental populations? I develop a formal analysis of several experimental and statistical techniques that are used to detect patterns of local and temporal adaptation. I provide recommendations regarding efficient experimental designs and statistical techniques to detect local adaptation. I also develop a new framework for the analysis of patterns of adaptation in time. I illustrate the potential use of this approach using a data set measuring the adaptation of HIV to the immune response of several recently infected patients. / Populations often experience environmental conditions that are variable both in space and in time. Understanding the demographic and evolutionary dynamics of populations in such variable environments has very practical implications for conservation biology, pest and pathogen control, management of antibiotic resistance. This thesis is an attempt to study the ecological and evolutionary implications of spatial and temporal variations of the environment.First, I study how spatially heterogeneous and temporally changing conditions influence the demographic dynamics of a genetically uniform population. The growth of the population is enhanced when individuals preferentially accumulate in high quality habitats. Migration between locations facilitates a good arrangement of individuals such that in general, an intermediate rate of migration maximizes the growth rate.Second, I develop a model where the growth rate of individuals depends on the environment but also on their genetic quality, and possibly on the interaction between the environment and the genotype. If the performance of different genotypes tradeoffs across the environments, several genotypes may be maintained locally in the environment that suit them and a pattern of local adaptation emerges. Moreover, I show that adaptation of populations to environmental fluctuations in the environment generates very dynamic changes in the genetic composition that lag behind the environmental change. Adaptation may be facilitated by the influx of migrants coming from other demes.How can we detect such patterns of adaptation in wild or experimental populations? I develop a formal analysis of several experimental and statistical techniques that are used to detect patterns of local and temporal adaptation. I provide recommendations regarding efficient experimental designs and statistical techniques to detect local adaptation. I also develop a new framework for the analysis of patterns of adaptation in time. I illustrate the potential use of this approach using a data set measuring the adaptation of HIV to the immune response of several recently infected patients.