In many scientific and engineering applications machine learning can leverage governing equations. The corresponding solutions are often called physically informed. In this context, mainly neural networks have been considered in view of their adaptivity properties. However, adaptivity comes at the expenses of more complex theoretical analysis. As a consequence a learning theory of physics informed learning is still in the making. In this paper, we consider kernel methods offering solutions more amenable to theoretical analysis. While reviewing a number of old and new ideas, we develop and analyze a class of Physics Informed Kernel Methods (PIKS). In physics informed problems,  solutions need to satisfy governing equations as a result they belong to suitable smoothness classes. Theoretical analysis typically assume the latter to be known a priori. But in many contexts this might not be the case resulting in model misspecification. Kernel methods are known to be universal learners for classical learning. In this paper, we show that analogous results hold for physics informed learning governed by linear differential operators. Our analysis develop the operator theoretic approach classical to analyze kernel methods to ensure governing equations are respected. Our theoretic analysis is complemented by numerical results contrasting PIKS with classical finite elements methods.