In strong-field and attosecond physics we face a number of fundamental challenges. I will address two. (i) How to deal with the nonperturbative strong-field driving of a multielectron system? (ii) Now to deal with situations, where standard approximations, like, e.g., the electric dipole approximation breaks down? Regarding (i), alternative approaches to the ab initio one are needed. I will discuss (a) tunneling theory based on a new integral formulation and (b) single-active-electron time-dependent Schrödinger-equation models including surprisingly simplifying and accurate multielectron polarization effects. Regarding (ii), I will discuss a strong-field-approximation Hamiltonian that is accurate for intense fields across high and low frequency regimes and which is on a form that can readily be dealt with numerically and analytically.