Tabular data embedded in PDF files, web pages, and other types of documents is prevalent in various domains. These tables, which we call human-centric tables (HCTs for short), are dense in information but often exhibit complex structural and semantic layouts. To query these HCTs, some existing solutions focus on transforming them into relational formats. However, they fail to handle the diverse and complex layouts of HCTs, making them not amenable to easy querying with SQL-based approaches. Another emerging option is to use Large Language Models (LLMs) and Vision Language Models (VLMs). However, there is a lack of standard evaluation benchmarks to measure and compare the performance of models to query HCTs using natural language. To address this gap, we propose the HumanCentric Tables Question-Answering extensive benchmark (HCTQA) consisting of thousands of HCTs with several thousands of natural language questions with their respective answers. More specifically, HCT-QA includes 1,880 real-world HCTs with 9,835 QA pairs in addition to 4,679 synthetic HCTs with 67.7K QA pairs. Also, we show through extensive experiments the performance of 25 and 9 different LLMS and VLMs, respectively, in an answering HCT-QA's questions. In addition, we show how finetuning an LLM on HCT-QA improves F1 scores by up to 25 percentage points compared to the off-the-shelf model. Compared to existing benchmarks, HCT-QA stands out for its broad complexity and diversity of covered HCTs and generated questions, its comprehensive metadata enabling deeper insight and analysis, and its novel synthetic data and QA generator.