Old Testament - Exodus

Indeed, incense is referred to frequently throughout both the Old and the New Testaments. In both the Old and the New Testaments, smoke from the incense is symbolic of the prayers of the faithful rising up to heaven; e.g.: 

"Let my prayer be incense before you; my uplifted hands an evening sacrifice."  (Psalm 141:2)

Smoke from incense in various Jewish and Christian liturgies also serves as a further reminder to the faithful of the presence of God as He manifested Himself in various theophanies throughout salvation history; e.g.: 

"Mount Sinai was all wrapped in smoke, for the Lord came down upon it in fire. The smokerose from it as though from a furnace, and the whole mountain trembled violently."   (Exodus 19:18)

In particular, Exodus 30:1-10 and Exodus 30:34-38 provide wonderful details that the Lord gave Moses for both constructing the altar of incense, and how to prepare the incense itself; e.g.: 

"On it Aaron shall burn fragrant incense. Morning after morning, when he prepares the lamps, and again in the evening twilight, when he lights the lamps, he shall burn incense. Throughout your generations this shall be the established incense offering before the Lord. On this altar you shall not offer up any profane incense..." (Exodus 30:7-9)

Of note is the admonition the Lord gives Moses not to use incense for profane purposes. The Lord again leaves Moses with similar admonitions regarding the proper preparation and use of the incense itself; i.e. 

"This incense shall be treated as most sacred by you. You may not make incense of a like mixture for yourselves; you must treat it as sacred to the Lord. Whoever makes an incense like this for his own enjoyment of its fragrance, shall be cut off from his kinsmen."   (Exodus 30:36-37)

 

Old Testament - Prophets 

Recalling God's commands to Moses, prophets like Isaiah, Jeremiah, Ezekiel and Hosea would later chastise the Israelites sternly for burning incense in a profane manner to false gods such as Baal, Ashtarte, Moloch, Chemosh, etc. rather than keeping it sacred and dedicated to God alone; e.g.: 

"Are you to steal and murder, commit adultery and perjury, burn incense to Baal,  go  after  strange gods that you know not, and yet  come  to stand before me in this  house  which  bears my name, and say: "We are safe; we can commit all these abominations again?"       (Jeremiah 7:9-10)

Smoke from incense during liturgical services (e.g. while singing the Sanctus at mass) also calls to mind other theophanies such as the prophet Isaiah's in which smoke accompanied the presence of God. i.e.:

"Holy, holy, holy is the LORD of hosts!" they cried to one another. "All the earth is filled with his glory!" At the sound of that cry, the frame of the door shook and the  house  was filled with smoke."  (Isaiah 6:3-4)

New Testament - Revelation

Then one of the four living creatures gave to the seven angels seven golden bowls
filled with the wrath of God, who lives for ever and ever. Rev. 15:7

In several places, the New Testament continues to draw our attention to the proper role incense plays as representative of the prayers of the faithful rising to heaven. A few examples are listed below. 

Luke:

"Once when he [Zechariah] was serving as priest in his division's turn before God, according to the practice of the priestly service, he was chosen by lot to enter the sanctuary of the Lord to burn incense. Then, when the whole assembly of the people was praying outside at the hour of the incense offering, the angel of the Lord appeared to him, standing at the right of the altar of incense."      (Luke 1:8-11)

Hebrews: 

"Now [even] the first covenant had regulations for worship and an earthly sanctuary. For a tabernacle was constructed, the outer one, in which were the lamp-stand, the table, and the bread of offering; this is called the Holy Place. Behind the second veil was the tabernacle called the Holy of Holies, in which were the gold altar of incense and the ark of the covenant entirely covered with gold."          (Hebrews 9:1-4)

Revelation:

"He came and received the scroll from the right hand of the one who sat on the throne. When he took it, the four living creatures and the twenty-four elders fell down before the Lamb. Each of the elders held a harp and gold bowls filled with incense, which are the prayers of the holy ones. "    (Revelation 5:6-8)

 

 

REFERENCES 

Confraternity of Christian Doctrine. The New American Bible, (Iowa Falls: IA, World Bible Publishers, Inc. 1991)