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In this paper, we outline our efficient sample- based approach to answer fixed-precision approximate continuous aggregate queries in peer-to-peer databases. We describe our approach in the context of Digest, a two-tier system we have developed for correct and efficient query answering by sampling. With Digest, at the top tier we develop a query evaluation engine that uses the samples collected from the peer-to-peer database to continually estimate the running result of the approximate continuous aggregate query with guaranteed precision. For efficient query evaluation, we propose an extrapolation algorithm that predicts the evolution of the running result and adapts the frequency of the continual sampling occasions accordingly to avoid redundant samples. We also introduce a repeated sampling algorithm that draws on the correlation between the samples at successive sampling occasions and exploits linear regression to minimize the number of the samples derived at each occasion. At the bottom tier, we introduce a distributed sampling algorithm for random sampling (uniform and nonuniform) from peer- to-peer databases with arbitrary network topology and tuple distribution. Our sampling algorithm is based on the Metropolis Markov Chain Monte Carlo method that guarantees randomness of the sample with arbitrary small variation difference with the desired distribution, while it is comparable to optimal sampling in sampling cost/time. We evaluate the efficiency of Digest via simulation using real data.