The concept of dual pairing vector spaces (DPVS) was introduced by Okamoto and Takashima in 2009, and it has been employed in various applications, functional encryption (FE) including attribute-based encryption (ABE) and inner-product encryption (IPE) as well as attribute-based signatures (ABS), generic conversion from composite-order group based schemes to prime-order group based ones and public-key watermarking. In this paper, we show the concept of DPVS, the major applications to FE and the key techniques employed in these applications. This paper presents them with placing more emphasis on plain and intuitive descriptions than formal preciseness.