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First, please note that Internet Explorer has been deprecated and replaced by Microsoft Edge for 4 years. It is not known to be a secure browser and has frequent major vulnerabilities. If your service provider doesn't support any modern cross-platform browser (such as Mozilla Firefox or Google Chrome), it may be time for a change of provider or service.

That being said, if you really must use Internet Explorer and since it's only available on Windows OS you only have three choices :

• Use a Windows PC or install Windows on your Mac using Bootcamp
• Use a virtualization software (VirtualBox, Parallel Desktop or VMware Fusion) to run Windows inside a virtual machine on macOS
• Use a compatibility layer to run windows programs on macOS without virtualization

That last choice may be a good alternative if you only want to run one specific program and don't need a full-fledged Windows running. Wine is a free and open-source solution capable of running windows program on Unix-like systems (Linux or macOS).

You can install and setup Wine manually but it's mostly dedicated for advanced system administrators. However, there are multiple packaged front-ends for Wine that allow running windows program on macOS without much technical knowledge :

• PlayOnMac, the Mac version of PlayOnLinux, is a free software and provides a user-friendly graphical interface with configuration templates to run the windows version of Internet Explorer
• CrossOver, a commercial solution with customer support if you have some money to spend. It also provides a graphical interface and may have better support than PlayOnMac.
• Winetricks, another open-source solution but mostly dedicated to advanced users

Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, possibly no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may still be the easier way to go.

FYI, I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :

It may very well be the best solution if PlayOnMac doesn't work and you don't have the technical background necessary to setup Wine manually and you don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.

First, please note that Internet Explorer has been deprecated and replaced by Microsoft Edge since 2015. It is not known to be a secure browser and has frequent major vulnerabilities. If your service provider doesn't support any modern cross-platform browser (such as Mozilla Firefox or Google Chrome), it may be time for a change of provider or service.

That being said, if you really must use Internet Explorer and since it's only available on Windows OS you only have three choices :

• Use a Windows PC or install Windows on your Mac using Bootcamp
• Use a virtualization software (VirtualBox, Parallel Desktop or VMware Fusion) to run Windows inside a virtual machine on macOS
• Use a compatibility layer to run windows programs on macOS without virtualization

That last choice may be a good alternative if you only want to run one specific program and don't need a full-fledged Windows running. Wine is a free and open-source solution capable of running windows program on Unix-like systems (Linux or macOS).

You can install and setup Wine manually but it's mostly dedicated for advanced system administrators. However, there are multiple packaged front-ends for Wine that allow running windows program on macOS without much technical knowledge :

• PlayOnMac, the Mac version of PlayOnLinux, is a free software and provides a user-friendly graphical interface with configuration templates to run the windows version of Internet Explorer
• CrossOver, a commercial solution with customer support if you have some money to spend. It also provides a graphical interface and may have better support than PlayOnMac.
• Winetricks, another open-source solution but mostly dedicated to advanced users

Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, possibly no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may still be the easier way to go.

FYI, I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :

It may very well be the best solution if PlayOnMac doesn't work and you don't have the technical background necessary to setup Wine manually and you don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.

An alternative to virtualization (which is already covered in other answer) would be to use a Windows runtime environment emulation such as Wine (free & open-source).

PlayOnMac, the Mac version of PlayOnLinux, is a free graphical frontend for Wine and provides configuration templates to run the windows version of Internet Explorer.

Alternatively, you can also install and setup Wine manually. It's mostly dedicated for advanced system administrator but there is a packaged commercial front-end called CrossOver with customer support if you have some money to spend.

Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may be the easier way to go.

Edit: I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :

It may very well be the best solution if PlayOnMac doesn't work and you don't have the technical background necessary to setup Wine manually and you don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.

First, please note that Internet Explorer has been deprecated and replaced by Microsoft Edge for 4 years. It is not known to be a secure browser and has frequent major vulnerabilities. If your service provider doesn't support any modern cross-platform browser (such as Mozilla Firefox or Google Chrome), it may be time for a change of provider or service.

That being said, if you really must use Internet Explorer and since it's only available on Windows OS you only have three choices :

• Use a Windows PC or install Windows on your Mac using Bootcamp
• Use a virtualization software (VirtualBox, Parallel Desktop or VMware Fusion) to run Windows inside a virtual machine on macOS
• Use a compatibility layer to run windows programs on macOS without virtualization

That last choice may be a good alternative if you only want to run one specific program and don't need a full-fledged Windows running. Wine is a free and open-source solution capable of running windows program on Unix-like systems (Linux or macOS).

You can install and setup Wine manually but it's mostly dedicated for advanced system administrators. However, there are multiple packaged front-ends for Wine that allow running windows program on macOS without much technical knowledge :

• PlayOnMac, the Mac version of PlayOnLinux, is a free software and provides a user-friendly graphical interface with configuration templates to run the windows version of Internet Explorer
• CrossOver, a commercial solution with customer support if you have some money to spend. It also provides a graphical interface and may have better support than PlayOnMac.
• Winetricks, another open-source solution but mostly dedicated to advanced users

Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, possibly no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may still be the easier way to go.

FYI, I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :

It may very well be the best solution if PlayOnMac doesn't work and you don't have the technical background necessary to setup Wine manually and you don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.

An alternative to virtualization (which is already covered in other answer) would be to use a Windows runtime environment emulation such as Wine (free & open-source).

PlayOnMac, the Mac version of PlayOnLinux, is a free graphical frontend for Wine and provides configuration templates to run the windows version of Internet Explorer.

Alternatively, you can also install and setup Wine manually. It's mostly dedicated for advanced system administrator but there is a packaged commercial front-end called CrossOver with customer support if you have some money to spend.

Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may be the easier way to go.

Edit: I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :

It may very well be the best solution if you don't have the technical background necessary to setup wine manually and don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.

An alternative to virtualization (which is already covered in other answer) would be to use a Windows runtime environment emulation such as Wine (free & open-source).

PlayOnMac, the Mac version of PlayOnLinux, is a free graphical frontend for Wine and provides configuration templates to run the windows version of Internet Explorer.

Alternatively, you can also install and setup Wine manually. It's mostly dedicated for advanced system administrator but there is a packaged commercial front-end called CrossOver with customer support if you have some money to spend.

Although those solutions have a lot of benefits (no virtual machine, no Windows license needed, no cost), they may be really tricky to set up if it doesn't work out-of-the-box. In which case a windows virtual machine may be the easier way to go.

Edit: I managed to run Internet Explorer 8 on macOS Mojave using the trial version of CrossOver :

It may very well be the best solution if PlayOnMac doesn't work and you don't have the technical background necessary to setup Wine manually and you don't want to spend ~$200 on a Parallel Desktop + Windows 10 VM solution.