This thesis addresses the problems of compression for the following data types: numbers, sequence of bits and webgraphs. For the problem of compression of a sequence of bits, we demonstrate the relationship between merge algorithms and binary source coders. Then, we show that the algorithms binary merge (Hwang and Lin, 1972), recursive merge (Dudzinski, 1981) and probabilistic merge (Vega, 1993), generate respectively an entropy coder based runlengths encoded with the Rice code, the interpolative binary coder (Moffat, 2000) and the random Rice coder, which is a new variant of the Rice code. For the problem of webgraph compression, we propose a new compact representation for webgraphs, entitled w-tree, built specifically for external memory (disk), being the first one in this genre. We also propose a new type of layout designed specifically for webgraphs, entitled scaled layout. In addition, we show how to build a cache-oblivious layout to explore the hierarchy of memories, being the first of its kind. We offer several types of queries that can be performed and it is the first representation to support batched random read query execution and advanced query optimization, including in main memory. Finally, we performed a series of experiments showing that the w-tree provides compression rates and running times competitive with other compact representations for main memory. Therefore, we demonstrate empirically the feasibility of a compact representation for external memory in practice, contrary to the assertion of several researchers (Suel, 2001) (Buehrer, 2008).