In this talk we will introduce new results concerning greedy-like bases. Concretely, we will talk about the characterization of greediness using polynomials of constant coefficients and, moreover, we will show some relations between approximation spaces and some greedy-like classes of approximation. The results presented in the talk are in some joint preprints with David González, Hung V. Chu, Miguel Berasategui and Eugenio Hernández.