Network monitoring has become a necessity to aid in the management and operation of large networks. Passive network monitoring consists of extracting metrics (or any information of interest) by analyzing the traffic that traverses one or more network links. Extracting information from a high-speed network link is challenging, given the great data volumes and short packet inter-arrival times. These difficulties can be alleviated by using extremely efficient algorithms or by sampling the incoming traffic. This work improves the state of the art in both these approaches. For one-way packet delay measurement, we propose a series of improvements over a recently appeared technique called Lossy Difference Aggregator. A main limitation of this technique is that it does not provide per-flow measurements. We propose a data structure called Lossy Difference Sketch that is capable of providing such per-flow delay measurements, and, unlike recent related works, does not rely on any model of packet delays. In the problem of collecting measurements under the sliding window model, we focus on the estimation of the number of active flows and in traffic filtering. Using a common approach, we propose one algorithm for each problem that obtains great accuracy with significant resource savings. In the traffic sampling area, the selection of the sampling rate is a crucial aspect. The most sensible approach involves dynamically adjusting sampling rates according to network traffic conditions, which is known as adaptive sampling. We propose an algorithm called Cuckoo Sampling that can operate with a fixed memory budget and perform adaptive flow-wise packet sampling. It is based on a very simple data structure and is computationally extremely lightweight. The techniques presented in this work are thoroughly evaluated through a combination of theoretical and experimental analysis.