Discrete Fourier transform spread orthogonal DFT-S-OFDM, adopted in 3GPP LTE uplink, enables the synthesis of block-based single carrier waveforms with various bandwidths by changing the size of the DFT-spread block. Conceptually, it also allows a transition between block-based multicarrier and single-carrier schemes when multiple DFT-spread blocks are employed in the structure. Recently, it has been shown that DFT-S-OFDM can also accommodate an internal guard period that offers flexibility on the duration of the guard periods without affecting the symbol duration. In this article, we present further modifications of DFT-S-OFDM that offer improvements in flexibility and discuss the latest enabling techniques on this topic. Considering the flexibility introduced by DFTs-OFDM and its variations, the DFT-S-OFDM family also offers a set of promising waveforms for 5G networks, which will require a flexible physical layer.