The enormous quantity of data produced every day together with advances in data analytics has led to a proliferation of data management and analysis systems. Typically, these systems are built around highly specialized monolithic operators optimized for the underlying hardware. While effective in the short term, such an approach makes the operators cumbersome to port and adapt, which is increasingly required due to the speed at which algorithms and hardware evolve. To address this limitation, we present Modularis, an execution layer for data analytics based on sub-operators, i.e.,composable building blocks resembling traditional database operators but at a finer granularity. To demonstrate the advantages of our approach, we use Modularis to build a distributed query processing system supporting relational queries running on an RDMA cluster, a serverless cloud platform, and a smart storage engine. Modularis requires minimal code changes to execute queries across these three diverse hardware platforms, showing that the sub-operator approach reduces the amount and complexity of the code. In fact, changes in the platform affect only sub-operators that depend on the underlying hardware. We show the end-to-end performance of Modularis by comparing it with a framework for SQL processing (Presto), a commercial cluster database (SingleStore), as well as Query-as-a-Service systems (Athena, BigQuery). Modularis outperforms all these systems, proving that the design and architectural advantages of a modular design can be achieved without degrading performance. We also compare Modularis with a hand-optimized implementation of a join for RDMA clusters. We show that Modularis has the advantage of being easily extensible to a wider range of join variants and group by queries, all of which are not supported in the hand-tuned join.