We shall report on some new developments concerning phi-FEM -- a fictitious domain finite element method first proposed in [1,2], cf. also an overview in [3] presenting several applications. The method is well suited for elliptic and parabolic problems posed in domains given by smooth level-set functions without constructing a mesh fitting the the boundary. phi-FEM achieves optimal convergence (attested both theoretically and numerically) using the finite elements of any order. Unlike other recent fictitious domain-type methods (XFEM, CutFEM), our approach does not need any non-standard numerical integration, neither on the cut mesh elements nor on the actual boundary. The main idea of phi-FEM is to extend the original problem slightly outside its domain (namely to the domain occupied by all the mesh cell having a non-empty intersection with the physical domain), and then write down a (formal) variational formulation on the extended domain using the level set to impose the boundary conditions "implicitly" (either via a product of the levelset with the finite elements or by introducing auxiliary variables). Some of the known issues of phi-FEM are: i) the necessity to increase the order of the numerical quadrature wrt the standard FEM; ii) relatively high conditioning numbers, in the case of Neumann boundary conditions. After presenting the general framework, we shall discuss the possible solutions to these issues. [1] Duprez, M. and Lozinski, A. $\phi$-FEM: a finite element method on domains defined by level-sets. SIAM J. Numer. Anal. 58 (2020) 1 pp. 1008-1028. [2] Duprez, M. and Lozinski, A and Lleras, V. A new $\phi$-FEM approach for problems with natural boundary conditions. Numer. Methods Partial Differ. Eq. 39 (2023) 1, pp. 281-303. [3] Cotin, S. and Duprez, M. and Lleras, V. and Lozinski, A. and Vuillemot, K. $\phi$-FEM: an efficient simulation tool using simple meshes for problems in structure mechanics and heat transfer, in Partition of Unity Methods, Wiley, 2023.