Apostles

Luke 6:13
And when it was day, He called His disciples to Himself; and from them He chose twelve whom He also named apostles:
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1 Cor 12:28-31
And God has appointed these in the church: first apostles, second prophets, third teachers, after that miracles, then gifts of healings, helps, administrations, varieties of tongues. 29 Are all apostles? Are all prophets? Are all teachers? Are all workers of miracles? 30 Do all have gifts of healings? Do all speak with tongues? Do all interpret? 31 But earnestly desire the best gifts.
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2 Cor 11:13-15
For such are false apostles, deceitful workers, transforming themselves into apostles of Christ. 14 And no wonder! For Satan himself transforms himself into an angel of light. 15 Therefore it is no great thing if his ministers also transform themselves into ministers of righteousness, whose end will be according to their works.
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Eph 4:11-13
And He Himself gave some to be apostles, some prophets, some evangelists, and some pastors and teachers, 12 for the equipping of the saints for the work of ministry, for the edifying of the body of Christ, 13 till we all come to the unity of the faith and of the knowledge of the Son of God, to a perfect man, to the measure of the stature of the fullness of Christ
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2 Cor 12:12
Truly the signs of an apostle were accomplished among you with all perseverance, in signs and wonders and mighty deeds.
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apostolos (ap-os'-tol-os); a delegate; specially, an ambassador of the Gospel; officially a commissioner of Christ ["apostle"] (with miraculous powers):

I do believe that there are apostles today. I believe that God calls some, by dreams or prophetic word. I believe there are those "sent out" from their church. And I believe that there are those who call themselves apostles because they want to lift themselves up, it is not from God.
I don't believe that apostles necessarily have to display signs and wonders as in 2 Cor 12. But I would caution people to be quick to accept someone who deems himself an apostle. Discernment is important at times.