[Edit October 2019] A couple of months after I wrote this answer, Koyama Kenta wrote a Kotlin targeted library which can be found at https://github.com/doyaaaaaken/kotlin-csv and which looks much better to me than opencsv.

Example usage: (for more info see the github page mentioned)

import com.github.doyaaaaaken.kotlincsv.dsl.csvReader

fun main() {
    csvReader().open("src/main/resources/test.csv") {
        readAllAsSequence().forEach { row ->
            //Do something
            println(row) //[a, b, c]
        }
    }
}

For a complete minimal project with this example, see https://github.com/PHPirates/kotlin-csv-reader-example

Old answer using opencsv:

As suggested, it is convenient to use opencsv. Here is a somewhat minimal example:

// You can of course remove the .withCSVParser part if you use the default separator instead of ;
val csvReader = CSVReaderBuilder(FileReader("filename.csv"))
        .withCSVParser(CSVParserBuilder().withSeparator(';').build())
        .build()

// Maybe do something with the header if there is one
val header = csvReader.readNext()

// Read the rest
var line: Array<String>? = csvReader.readNext()
while (line != null) {
    // Do something with the data
    println(line[0])

    line = csvReader.readNext()
}

As seen in the docs when you do not need to process every line separately you can get the result in the form of a Map:

import com.opencsv.CSVReaderHeaderAware
import java.io.FileReader

fun main() {
    val reader = CSVReaderHeaderAware(FileReader("test.csv"))
    val resultList = mutableListOf<Map<String, String>>()
    var line = reader.readMap()
    while (line != null) {
        resultList.add(line)
        line = reader.readMap()
    }
    println(resultList)
    // Line 2, by column name
    println(resultList[1]["my column name"])
}

Dependency for Gradle: compile 'com.opencsv:opencsv:4.6' or for Gradle Kotlin DSL: compile("com.opencsv:opencsv:4.6") (as always, check for latest version in docs).