If you have both programs, i.e. CorelDraw and Adobe Illustrator, you can export to AI or PDF directly from CorelDraw and then open or import the file to Adobe Illustrator. On top of that, you may also exchange graphics parts through clipboard or export to other common vector graphics and then import it to Illustrator.
The important question for the success of the conversion is, how the artwork created in Corel was exported. If you need to work with layers, go to Tools ► Object manager and create all layer you need and each object will be stored in the layer you have selected. Illustrator will preserve all the layers from CorelDRAW, so when you export your artwork as Illustrator's AI format, select the proper Illustrator version (the one you have installed, instead the default version offered by default in CorelDRAW.
Many versions of CorelDRAW exists and thus many versions of CDR format and it is always best to use the latest version of the program. Current (at the time of writing this text) version of CorelDRAW X7 supports direct saving to Adobe Illustrator format through the File ► Save as.. and export cdr graphics to ai.
Alternatively, you can convert CDR graphics to AI graphics using some third party programs, such as UniConverter.
However, as Corel's CDR format is proprietary and closed, the end result won't most likely be perfect, because the latest version of CDR format is rarely supported outside CorelDRAW. In most cases, the more recent the CDR format is, the worse the odds for successful conversion are.