The Greek word apostolos simply means “messenger.” For instance, sometimes the NT uses this word to simply refer to regular messengers. Paul calls Epaphroditus (Phil. 2:25) and Titus (2 Cor. 8:23) “messengers” to churches, but not authoritative apostles. He also refers to two “apostles” in the church at Rome (Rom. 16:7).
But while this term is used in a broad sense in the NT, it is also used in a very specific sense. That is, there was a closed fraternity of apostles in the first-century that do not exist today. Theologian Wayne Grudem notes that there were two qualifications of being an apostle: (1) seeing the risen Christ and (2) having been selected by Christ.
CRITERION #1: Seeing Jesus risen
The apostles needed to see Jesus risen from the dead in order to be an apostle. Jesus “presented Himself alive after His suffering, by many convincing proofs” to the apostles (Acts 1:2-3). Later, they “were giving testimony to the resurrection of the Lord Jesus” (Acts 4:33).
After Judas’ death, Peter claimed that the replacement needed to be “a witness with us of His resurrection” (Acts 1:22). Paul said that he was an apostle, because he had seen Jesus risen from the dead (1 Cor. 9:1). This was the basis for James’ apostleship as well (1 Cor. 15:7).
CRITERION #2: Selection by Jesus
In addition to seeing Jesus, an individual needed to be selected by Jesus, in order to be an apostle. Originally, Jesus sent the apostles on their mission to the cities in Judea (Mt. 10:1-7). After his resurrection, Jesus selected the disciples. He said, “You shall be My witnesses both in Jerusalem, and in all Judea and Samaria, and even to the remotest part of the earth” (Acts 1:8). The apostles believed the Judas’ replacement needed to be “chosen” by Jesus (Acts 1:24). Likewise, Paul believed that he was an apostle because Jesus had “chosen” and “called” him to this role (Rom. 1:1; Gal. 1:1; 1 Tim. 1:12; 2:7; 2 Tim. 1:11).
How many apostles were there?
Based on the criteria above, there could have been more than twelve apostles. For one, Paul was an apostle—even though he wasn’t one of the Twelve. Moreover, Barnabas was called an apostle (Acts 14:14). James was called an apostle, on par with Peter and John (Gal. 1:19). In fact, James is called a “pillar” of the early church (Gal. 2:9), and he played a significant role in the early church (Acts 15). Apparently, Jesus appeared to James (1 Cor. 15:7), as well as the rest of the apostles (1 Cor. 15:8-9). In fact, there could have been many apostles, because Jesus appeared to 500 people (1 Cor. 15:6), though not all were selected by Christ (see Criterion #2 above). Though Grudem writes, “Were there more than these fifteen? There may possibly have been a few more, though we know little if anything about them, and it is not certain that there were any more.”
 Grudem, Wayne. Systematic Theology. Grand Rapids, MI. Zondervan Publishing House. 1994. 906.
 Grudem, Wayne. Systematic Theology. Grand Rapids, MI. Zondervan Publishing House. 1994. 908.