The blog post delves into the intricacies of Elasticsearch's query and filter execution processes, challenging the common misconception that filters always precede queries. It explains that execution involves two phases: an initial approximation phase using operations like `nextDoc` and `advance`, followed by a verification phase using `matches`. The post highlights that the order of execution is determined by factors such as cost and match cost, rather than a fixed sequence, as illustrated through examples like term queries, disjunctions, conjunctions, and phrase queries. The document underscores the importance of metadata from the inverted index, such as term and document frequencies, in optimizing execution order. It clarifies that while the order of queries and filters in the query DSL does not impact execution, the system automatically reorders them based on their respective costs, and ultimately, execution is interleaved to ensure efficiency.