Databases in the past have helped businesses maintain and extract insights from their data. Today, it is common for a business to involve multiple independent, distrustful parties. This trend towards decentralization introduces a new and important requirement to databases: the integrity of the data, the history, and the execution must be protected. In other words, there is a need for a new class of database systems whose integrity can be verified (or verifiable databases). In this paper, we identify the requirements and the design challenges of verifiable databases.We observe that the main challenges come from the need to balance data immutability, tamper evidence, and performance. We first consider approaches that extend existing OLTP and OLAP systems with support for verification. We next examine a clean-slate approach, by describing a new system, Spitz, specifically designed for efficiently supporting immutable and tamper-evident transaction management. We conduct a preliminary performance study of both approaches against a baseline system, and provide insights on their performance.