Sketching techniques are widely adopted in network applications. Sketching algorithms “encode” data into succinct data structures that can later be accessed and “decoded” for various purposes, such as network measurement, accounting, anomaly detection and etc. Bloom filters and counter braids are two well-known representatives in this category. Those sketching algorithms usually need to strike a tradeoff between performance (how much information can be revealed and how fast) and cost (storage, transmission and computation). This dissertation is dedicated to the research and development of several sketching techniques including improved forms of stateful Bloom Filters, Statistical Counter Arrays and Error Estimating Codes. Bloom filter is a space-efficient randomized data structure for approximately representing a set in order to support membership queries. Bloom filter and its variants have found widespread use in many networking applications, where it is important to minimize the cost of storing and communicating network data. In this thesis, we propose a family of Bloom Filter variants augmented by rank-indexing method. We will show such augmentation can bring a significant reduction of space and also the number of memory accesses, especially when deletions of set elements from the Bloom Filter need to be supported. Exact active counter array is another important building block in many sketching algorithms, where storage cost of the array is of paramount concern. Previous approaches reduce the storage costs while either losing accuracy or supporting only passive measurements. In this thesis, we propose an exact statistics counter array architecture that can support active measurements (real-time read and write). It also leverages the aforementioned rank-indexing method and exploits statistical multiplexing to minimize the storage costs of the counter array. Error estimating coding (EEC) has recently been established as an important tool to estimate bit error rates in the transmission of packets over wireless links. In essence, the EEC problem is also a sketching problem, since the EEC codes can be viewed as a sketch of the packet sent, which is decoded by the receiver to estimate bit error rate. In this thesis, we will first investigate the asymptotic bound of error estimating coding by viewing the problem from two-party computation perspective and then investigate its coding/decoding efficiency using Fisher information analysis. Further, we develop several sketching techniques including Enhanced tug-of-war(EToW) sketch and the generalized EEC (gEEC)sketch family which can achieve around 70% reduction of sketch size with similar estimation accuracies. For all solutions proposed above, we will use theoretical tools such as information theory and communication complexity to investigate how far our proposed solutions are away from the theoretical optimal. We will show that the proposed techniques are asymptotically or empirically very close to the theoretical bounds.