Nowadays stream analysis is used in many context where the amount of data and/or the rate at which it is generated rules out other approaches (e.g., batch processing). The data streaming model provides randomized and/or approximated solutions to compute specific functions over (distributed) stream(s) of data-items in worst case scenarios, while striving for small resources usage. In particular, we look into two classical and related data streaming problems: frequency estimation and (distributed) heavy hitters. A less common field of application is stream processing which is somehow complementary and more practical, providing efficient and highly scalable frameworks to perform soft real-time generic computation on streams, relying on cloud computing. This duality allows us to apply data streaming solutions to optimize stream processing systems. In this thesis, we provide a novel algorithm to track heavy hitters in distributed streams and two extensions of a well-known algorithm to estimate the frequencies of data items. We also tackle two related problems and their solution: provide even partitioning of the item universe based on their weights and provide an estimation of the values carried by the items of the stream. We then apply these results to both network monitoring and stream processing. In particular, we leverage these solutions to perform load shedding as well as to load balance parallelized operators in stream processing systems.