Whom do the Jews believe that Isaiah is referring to in chapter 53?

Isaiah 53 very clearly describes the Messiah who paid the ultimate price for the sins of Israel and the world. This is a difficult chapter for the Jews who do not believe that Jesus is the Messiah. They try to identify the suffering servant as the Jews. While on one hand this could be understood because the Jews have suffered more than any other group of people, this Scripture is not referring to a group of people; it's referring to an individual, a man named Jesus Christ.

It is impossible to deny that this passage is describing Jesus. Verse 7 says, “...he is brought as a lamb to the slaughter, and as a sheep before her shearers is dumb, so he openeth not his mouth.” He was crucified between two robbers. Verse 9 says, “...he made his grave with the wicked...” and was buried in a rich man's tomb, “...and with the rich in his death....” Peter wrote, “Who did no sin, neither was guile found in his mouth” (1st Peter 2:22). Isaiah testified, “Neither was any deceit in his mouth” and the last verse again mentions the two criminals he was crucified between: “...he was numbered with the transgressors; and he bare the sin of many, and made intercession for the transgressors.” This chapter contains too many details that describe a person, a man, that cannot apply to a nation or group of people.

How will the statement, “...they shall look upon Him whom they have pierced,” be fulfilled when those who were alive at Jesus' crucifixion are long gone?

This refers to the identity of a people: Israel. Until this day, the Jewish people blatantly reject the truth that Jesus is the Messiah. Romans 11:28 says, “As concerning the gospel, they are enemies for your sakes: but as touching the election, they are beloved for the fathers' sakes.” So as a people--to be precise, God's chosen people--they pierced Him and still reject Him until this very day, although the actual piercing was done by a Roman soldier. Here we see demonstrated a national, collective guilt. A more modern example would be to say that the Germans killed the Jews; however, virtually no one who actually did the killing is alive today, yet the guilt is still there and the Germans will have to deal with that guilt for many years to come.