This paper studies the problem of finding objects with durable quality over time in historical time series databases. For example, a sociologist may be interested in the top 10 web search terms during the period of some historical events; the police may seek for vehicles that move close to a suspect 70% of the time during a certain time, etc. Durable top-k (DTop-k) and nearest neighbor (DkNN) queries can be viewed as natural extensions of the standard snapshot top-k and NN queries to timestamped sequences of values or locations. Although their snapshot counterparts have been studied extensively, to our knowledge, there is little prior work that addresses this new class of durable queries. Existing methods for DTop-k processing either apply trivial solutions, or rely on domain-specific properties. Motivated by this, we propose efficient and scalable algorithms for the DTop-k and DkNN queries, based on novel indexing and query evaluation techniques. Our experiments show that the proposed algorithms outperform previous and baseline solutions by a wide margin.