Classical mechanics (CM) does not apply to arbitrary bodies in arbitrary states, such as superfluids like liquid helium, which exhibit non-classical properties like quantized vorticity. This motivates the introduction of the concept of a classical body, which satisfies CM within experimental error. Quantum fluids may require quantum continuum mechanics, which could be based on atomic-statistical theories. However, CM remains valuable as a theory of bulk matter because it is largely insensitive to the specific atomic structure. Its weakness is its strength. Classical field theories involve fields (scalar, vector, tensor, or spinor) and are based on action principles with lagrangian densities. A real field must be transformable only locally, not globally. For example, the Coriolis acceleration is not a real field because it can be transformed away by choosing a rotating reference frame, whereas a magnetic field is real because it cannot be transformed away. A physical field theory uses mathematical fields, postulates laws with invariance properties, and assumes fields refer to extended, massless substances. Thermodynamics and other continuum theories are material field theories, referring to extended material systems. Pure field theories, like special relativity, do not refer to material substrata. The distinction between pure and material field theories is not a dichotomy, as macroelectromagnetism is a mixed field theory. Field theories raise philosophical questions, particularly about the justification of fields. Fields are unobservable and thus metaphysical, but they are introduced as primitives and measured indirectly. The concept of fields is often confused with test bodies, leading to subjectivistic views. The truth is that field strengths are not defined in mechanical terms but are introduced as primitives and measured through their effects.Classical mechanics (CM) does not apply to arbitrary bodies in arbitrary states, such as superfluids like liquid helium, which exhibit non-classical properties like quantized vorticity. This motivates the introduction of the concept of a classical body, which satisfies CM within experimental error. Quantum fluids may require quantum continuum mechanics, which could be based on atomic-statistical theories. However, CM remains valuable as a theory of bulk matter because it is largely insensitive to the specific atomic structure. Its weakness is its strength. Classical field theories involve fields (scalar, vector, tensor, or spinor) and are based on action principles with lagrangian densities. A real field must be transformable only locally, not globally. For example, the Coriolis acceleration is not a real field because it can be transformed away by choosing a rotating reference frame, whereas a magnetic field is real because it cannot be transformed away. A physical field theory uses mathematical fields, postulates laws with invariance properties, and assumes fields refer to extended, massless substances. Thermodynamics and other continuum theories are material field theories, referring to extended material systems. Pure field theories, like special relativity, do not refer to material substrata. The distinction between pure and material field theories is not a dichotomy, as macroelectromagnetism is a mixed field theory. Field theories raise philosophical questions, particularly about the justification of fields. Fields are unobservable and thus metaphysical, but they are introduced as primitives and measured indirectly. The concept of fields is often confused with test bodies, leading to subjectivistic views. The truth is that field strengths are not defined in mechanical terms but are introduced as primitives and measured through their effects.