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The dissertation deals with noncommutative field theories, namely fieldtheories compatible with the existence of a minimal (quantum gravity) lengthscale. Two families of quantum spacetime are considered. One is characterizedby semisimple Lie algebras of coordinates. The other is characterized bysolvable Lie algebras. The explicit construction of corresponding Weyl-likestar products is given. We then focus on two specific examples of quantum spaceand study the quantum properties of various models of scalar field theory withquartic interactions built on them. The corresponding 2-point and 4-pointfunctions are computed at one-loop and the UV/IR mixing is discussed. The firstquantum spacetime considered is known as $\mathbb{R}^3_\theta$ which is adeformation of $\mathbb{R}^3$ with $\mathfrak{su}(2)$ noncommutativity. In thiscase, the one-loop 2-point function is found to be finite with the deformationparameter playing the role of a cutoff. The second quantum space is known as$\kappa$-Minkowski. In this case, the action functional is required$\kappa$-Poincar\'e invariant and various kinetic operators are considered. Inone case, we find that the one-loop 2-point function has milder UV divergencethan in the commutative case and that the one-loop 4-point function is finite.The renormalization properties are discussed. Besides, the loss of cyclicity ofthe Lebesgue integral (which results from the $\kappa$-Poincar\'e invariance ofthe action functional) is interpreted as reflecting the occurrence of KMScondition at the level of the algebra of fields modelling $\kappa$-Minkowski.This interpretation sheds new light on $\kappa$-deformation-based quantumgravity models, and solved a 25 years old problem in the study of$\kappa$-Poincar\'e invariant quantum field theories. Possible extensions ofthis work are finally discussed.

On the quantum structure of spacetime and its relation to the quantum  theory of fields: $\kappa$-Poincar\'e invariant field theories and other  examples