Polynomial Identity Testing (PIT) algorithms have focused on polynomials computed either by small alternation-depth arithmetic circuits, or by read-restricted formulas. Read-once polynomials (ROPs) are computed by read-once formulas (ROFs) and are the simplest of read-restricted polynomials. Building structures above these, we show the following: \begin{enumerate} \item A deterministic polynomial-time non-black-box PIT algorithm for (2) RO F . \item Weak hardness of representation theorems for sums of powers of constant-free ROPs and for ROPs of the form . \item A partial characterization of multilinear monotone constant-free ROPs. \end{enumerate}