We extend the No-Core Shell Model (NCSM) methodology to incorporate strangeness degrees of freedom and apply it to single-Λ hypernuclei. After discussing the transformation of the hyperon-nucleon (YN) interaction into Harmonic-Oscillator (HO) basis and the Similarity Renormalization Group transformation applied to it to improve model-space convergence, we present two complementary formulations of the NCSM, one that uses relative Jacobi coordinates and symmetry-adapted basis states to fully exploit the symmetries of the hypernuclear Hamiltonian, and one working in a Slater determinant basis of HO states where antisymmetrization and computation of matrix elements is simple and to which an importance-truncation scheme can be applied. For the Jacobi-coordinate formulation, we give an iterative procedure for the construction of the antisymmetric basis for arbitrary particle number and present the formulae used to embed two-and three-baryon interactions into the many-body space. For the Slater-determinant formulation, we discuss the conversion of the YN interaction matrix elements from relative to single-particle coordinates, the importance-truncation scheme that tailors the model space to the description of the low-lying spectrum, and the role of the redundant center-of-mass degrees of freedom. We conclude with a validation of both formulations in the four-body system, giving converged ground-state energies for a chiral Hamiltonian, and present a short survey of the A ≤ 7 hyper-helium isotopes. PACS numbers: 21.80.+a, 21.10.Dr, 21.60.De, 05.10.CcStrangeness impacts many fields of physics from heavy-ion collisions to nuclear and neutron star structure. Of particular interest are hypernuclei, which can be produced and studied in the laboratory. Hypernuclei are many-body systems consisting of nucleons and hyperons, baryons that carry strangeness, like the Λ 0 , Σ 0,± , or the Ξ 0,− . These hyperons are distinguishable from the nucleons and can be used as probes for the interior structure of the nucleonic core. Furthermore, hypernuclei extend the isospin SU(2), which is a good approximate symmetry in nuclei, to flavor SU(3) that is broken by the significant mass difference between the strange and the up and down quarks [1]. This breaking allows new types of baryonbaryon interactions such as antisymmetric spin-orbit forces, which are forbidden by isospin symmetry [2].A variety of experiments were performed to study properties of hypernuclei. From the early emulsion experiments (see, e.g., Ref.[3]) to modern accelerator-based experiments, a lot of effort went into the measurement of not only ground-state properties [4][5][6][7][8][9], but also the determination of hypernuclear spectra by gamma-ray spectroscopy [10][11][12][13][14]. Even transition strengths are experimentally accessible [15]. This effort was complemented by various theory developments, e.g., Skyrmeand Brueckner-Hartree-Fock models [16][17][18], the shell model [19][20][21][22][23][24], cluster models [25][26][27][28], and few-body methods [29][30][31][32][3...