In recent years, emerging hardware storage technologies have focused on divergent goals: better performance or lower cost-per-bit of storage. Correspondingly, data systems that employ these new technologies are optimized either to be fast (but expensive) or cheap (but slow). We take a different approach: by combining multiple tiers of fast and low-cost storage technologies within the same system, we can achieve a Pareto-efficient balance between performance and cost-per-bit. This paper presents the design and implementation of PrismDB, a novel log-structured merge tree based key-value store that exploits a full spectrum of heterogeneous storage technologies (from 3D XPoint to QLC NAND). We introduce the notion of read-awareness to log-structured merge trees, which allows hot objects to be pinned to faster storage, achieving better tiering and hot-cold separation of objects. Compared to the standard use of RocksDB on flash in datacenters today, PrismDBs average throughput on heterogeneous storage is 2.3$times$ faster and its tail latency is more than an order of magnitude better, using hardware than is half the cost.