Abstract : This work concerns the theoretical and numerical study of Chebyshevian splines. These functions generalize the polynomial splines and preserve most of their properties. Moreover, Chebyshevian splines have turned out to be useful in geometric design due to the shape parameters they provide. Firstly, we study the splines based on translation invariant Chebyshevian spaces. Then we show, under some conditions, that the Chebyshevian B-spline bases are orthonormal in a weighted Sobolev space associated with unique sequence of positive real numbers. Due to the properties of the B-splines, the best approximation in the space of Chebyshevian splines with respect to the associated norm is then a local projector. Finally, for the numerical implementation of the previous results, we use an adapted quadrature method. Some examples illustrating the possible shape effects are presented. These results extend the results recently obtained by Ulrich Reif in the particular case of polynomial splines.