Numerical data plays a crucial role in various real-world domains like finance, economics, and science. Thus, understanding and reasoning with numbers are essential in these fields. Recent benchmarks have assessed the numerical reasoning abilities of language models, revealing their limitations in limited and specific numerical aspects. In this paper, we propose a complete hierarchical taxonomy for numerical reasoning skills, encompassing over ten reasoning types across four levels: representation, number sense, manipulation, and complex reasoning. We conduct a comprehensive evaluation of state-of-the-art models on all reasoning types. To identify challenging reasoning types for different model types, we develop a diverse and extensive set of numerical probes and measure performance shifts. By employing a semi-automated approach, we focus on the tabular Natural Language Inference (TNLI) task as a case study. While no single model excels in all reasoning types, FlanT5 (few-/zero-shot) and GPT3.5 (few-shot) demonstrate strong overall numerical reasoning skills compared to other models in our probes.