Logical Captcha takes advantage of the TextCaptcha.com service, which provides logic-based textual questions instead of distorted images or audio to validate that the entity registering is a real live human being, and not a spam bot. It will provide protection against false registrations and the dreaded spam comments, etc.
An example of such a question might be:
Question: 
Out of a truck, a lion, the color purple, and the number forty-two, which has a door?
Answer: 
truck
Textual logic-based captchas mean that your registration process will be accessible to everyone, including visually/hearing impaired visitors who use access technology to surf the web. It requires a free API key from <a href="http://TextCaptcha.com" rel="nofollow ugc">TextCaptcha.com</a>
This plugin was developed by Josh de Lioncourt of <a href="http://maccessibility.net" rel="nofollow ugc">the Mac-cessibility Network</a>, a site dedicated to blind and visually impaired users of the Mac OS X operating system, the iPhone OS, and other Apple Inc. products and services. Josh de Lioncourt, the Mac-cessibility Network, and related sites are not in anyway affiliated with TextCaptcha.com

Logical Captcha

Integrates a logic captcha to verify that the registrant is a human and not a spam bot instead of using distorted images or audio.

Max K

Easy to integrate modal with Login and Registration features + inline form using shortcode. Compatible with any theme.
<a href="https://demo.maxim-kaminsky.com/lrm/" rel="nofollow ugc">DEMO >></a>
Features:
<ol>
<li>Easy to integrate (as modal or inline via shortcode)</li>
<li>Well customized</li>
<li>100% responsive</li>
<li>Beautifully coded</li>
<li>Compatible with other plugins (WooCommerce, BuddyPress, Ultimate Member, WPML, etc)</li>
<li>Tested with the latest WP version</li>
<li>Compatible with the Gutenberg</li>
<li>Possible to replace wp-login.php with a custom “Login”, “Registration” and “Reset password” pages</li>
<li>Skins support (1 default skin + 2 new in a PRO version) + possible to customize Skins colors via WP Customizer</li>
<li>Powerful after-login/registration/logout actions (reload, redirects, etc)</li>
<li>Role-based redirects (in PRO)</li>
<li>In-build reCaptcha & MatchCaptcha (in PRO)</li>
<li>Google Authenticator plugin & Wordfence 2FA support (in PRO)</li>
<li>Developer support (via forums or personal via email for PRO users)</li>
</ol>
Customization options:
<ol>
<li>You can add your custom CSS selectors to attach modal</li>
<li>All texts/messages can be edited/translated in settings</li>
<li>Emails (for registration and lost password) can customized in settings7</li>
</ol>
Free version compatible with (and other, this is 100% tested):
<ol>
<li><a href="https://wordpress.org/plugins/login-lockdown/" rel="ugc">Login LockDown</a> (limit login attempts count)</li>
<li><a href="https://wordpress.org/plugins/wp-facebook-login/" rel="ugc">WP Facebook Login</a></li>
<li><a href="https://wp-vote.net/wordpress-voting-plugin/" rel="nofollow ugc">WP Foto Vote contests</a> (photo contest plugin from author of this plugin ☺)</li>
<li><a href="https://wordpress.org/plugins/all-in-one-wp-security-and-firewall/" rel="ugc">All In One WP Security & Firewall</a> (tested with “Renamed Login Page”)</li>
<li><a href="https://wordpress.org/plugins/eonet-manual-user-approve/" rel="ugc">Eonet Manual User Approve</a>: review user before they an sign in – <a href="https://docs.maxim-kaminsky.com/lrm/kb/how-to-manually-review-new-users-registrations/" rel="nofollow ugc">tutorial</a></li>
<li><a href="https://wpml.org/" rel="nofollow ugc">WPML</a>: Multi-language support – <a href="https://docs.maxim-kaminsky.com/lrm/kb/multi-language-support-via-wpml/" rel="nofollow ugc">tutorial</a></li>
<li><a href="https://wordpress.org/plugins/weglot/" rel="ugc">Weglot translation plugin</a> – <a href="https://docs.maxim-kaminsky.com/lrm/kb/weglot-support/" rel="nofollow ugc">tutorial</a></li>
<li><a href="https://wordpress.org/plugins/s2member/" rel="ugc">s2member</a> plugin: tweaks for login process</li>
<li><a href="https://wordpress.org/plugins/new-user-approve/" rel="ugc">New User Approve </a> plugin: review approve new users registrations</li>
</ol>
Roadmap
<ul>
<li>+Allow including form to page content (without modal) (done in version 1.41)</li>
<li>+Colors/styles customizer [implemented via WP Customizer]</li>
<li>+Documentation and Videos [done] – https://docs.maxim-kaminsky.com/lrm/</li>
<li>+WooCommerce Login/Registration form integration (done in PRO version 1.28)</li>
<li>Registration Form builder</li>
<li>+Settings Import/Export [done]</li>
</ul>
<h4>PRO features</h4>
<ul>
<li>6-month personal support from the developer via Email</li>
<li>Troubleshooting problems and conflicts with other plugins/themes</li>
<li>Unlimited plugin updates</li>
<li>Compatibility with other popular plugins (list below)</li>
</ul>
The PRO version extra features:
<ol>
<li>Allow user to set a custom password (not randomly generated) during registration</li>
<li>Redirect the user to the specified page after login/registration/logout (for example to the User Profile)</li>
<li>User verification via click on the link in registration email</li>
<li>Email only registration – hide username filed from registration form</li>
<li>Customize button color in <a href="https://docs.maxim-kaminsky.com/lrm/kb/how-to-customize-form-colors-pro-only/" rel="nofollow ugc">WP Customizer</a></li>
<li><a href="https://maxim-kaminsky.com/shop/contact-me/" rel="nofollow ugc">Request other feature >></a></li>
</ol>
The PRO version is 100% tested and are compatible with a following plugins:
<ol>
<li><a href="https://wordpress.org/plugins/wordfence/" rel="ugc">Wordfence & Wordfence Login Security</a> (2 factor login – <a href="https://docs.maxim-kaminsky.com/lrm/kb/2-factor-login-otp-verification/" rel="nofollow ugc">example</a>)</li>
<li><a href="https://wordpress.org/plugins/woocommerce/" rel="ugc">WooCommerce</a> (show modal when clicked “Add to cart” in list or single product or in Cart when click “Process to Checkout”, option to replace WC account login/registration form to plugin ajax form)</li>
<li><a href="https://woocommerce.com/products/sensei/" rel="nofollow ugc">WooCommerce Sensei</a> (fix for Login process)</li>
<li><a href="https://wordpress.org/plugins/wp-recaptcha-integration/" rel="ugc">WP reCaptcha Integration</a></li>
<li><a href="https://wordpress.org/plugins/invisible-recaptcha/" rel="ugc">Invisible reCaptcha</a> – <a href="https://docs.maxim-kaminsky.com/lrm/kb/how-to-set-up-invisible-recaptcha/" rel="nofollow ugc">tutorial</a></li>
<li><a href="https://wordpress.org/plugins/buddypress/" rel="ugc">BuddyPress</a> (<a href="https://monosnap.com/file/3RNMa7Wl3EYWidw9znAJbgJ5QVL7oy" rel="nofollow ugc">replace default registration form with BuddyPress one >></a>)</li>
<li><a href="https://wordpress.org/plugins/ultimate-member/" rel="ugc">UltimateMember</a> (<a href="https://monosnap.com/file/a2RxnzawR2N9qBdyKJMxh8J5ALuaYs" rel="nofollow ugc">replace default registration form with UltimateMember one >></a>)</li>
<li><a href="https://wordpress.org/plugins/captcha/" rel="ugc">Captcha</a></li>
<li><a href="https://wordpress.org/plugins/really-simple-captcha/" rel="ugc">Really Simple CAPTCHA</a></li>
<li><a href="https://ru.wordpress.org/plugins/captcha-bank/" rel="nofollow ugc">Captcha bank</a></li>
<li><a href="https://wordpress.org/plugins/wordpress-social-login/" rel="ugc">WordPress Social Login</a> (social login buttons below login/register form)</li>
<li><a href="https://wordpress.org/plugins/accesspress-social-login-lite/" rel="ugc">Social Login WordPress Plugin – AccessPress</a> (social login buttons below login/register form)</li>
<li><a href="https://wordpress.org/plugins/super-socializer/" rel="ugc">WordPress Social Share, Social Login and Social Comments Plugin – Super Socializer</a> (social login buttons below login/register form, social share, etc)</li>
<li><a href="https://wordpress.org/plugins/super-socializer/" rel="ugc">WordPress Social Share, Social Login and Social Comments Plugin – Super Socializer</a> (social login buttons below login/register form, social share, etc)</li>
<li><a href="https://jetpack.com/support/sso/" rel="nofollow ugc">Jetpack – SSO login</a> <a href="https://monosnap.com/file/4Na5FYYONRj79jnLBmQFK3hjnMJQDR" rel="nofollow ugc">WordPress.com login button >></a></li>
<li><a href="https://wordpress.org/plugins/wc-vendors/" rel="ugc">WC Vendors & WC Vendors Pro</a> <a href="https://monosnap.com/file/TmpY4bYTHwF36ouN6fGpdjKZi5k3jz" rel="nofollow ugc">Apply to become vendor checkbox >></a></li>
<li><a href="https://wordpress.org/plugins/mailchimp-for-wp/" rel="ugc">MailChimp for WordPress</a> <a href="https://monosnap.com/file/sVpsvTnIzQoplRA7ap3IBPfb81kPuV" rel="nofollow ugc">Subscribe to newsletter checkbox >></a></li>
<li><a href="https://wordpress.org/plugins/google-authenticator/" rel="ugc">Google Authenticator</a> <a href="https://docs.maxim-kaminsky.com/lrm/kb/2-factor-login-otp-verification/" rel="nofollow ugc">Google Authenticator field during the login</a></li>
<li><a href="https://www.gravityforms.com/add-ons/user-registration/" rel="nofollow ugc">Gravity Forms + Gravity Forms User Registration Add-On</a> <a href="https://docs.maxim-kaminsky.com/lrm/kb/gravity-forms-integration/" rel="nofollow ugc">Replace with Gravity Forms registration form</a></li>
<li>Easy Digital Downloads – soon</li>
<li><a href="https://maxim-kaminsky.com/shop/contact-me/" rel="nofollow ugc">Request other plugin >></a></li>
</ol>
<a href="https://maxim-kaminsky.com/shop/product/ajax-login-and-registration-modal-popup-pro/" rel="nofollow ugc">GET PRO >></a>
<a href="https://demo.maxim-kaminsky.com/lrm/pro/" rel="nofollow ugc">PRO DEMO >></a>
<h3>Known issues</h3>
<ul>
<li>With Theme my login (TML) plugin (3 Password fields on the Create Account tab, if enable password field in LRM and TML)</li>
</ul>

AJAX Login and Registration modal popup + inline form

Free version worked well, I purchased the Pro version shortly afterwards, really pleased with this.

Using this for the first time on a site with dozens of other plugins, absolutely no conflicts, styling looks great, everything works well.

The only thing I would like to see is improvement with the admin menus. The menu structure isn't exactly clear, and the menu styling isn't really in keeping with anything else. With that said, all the user facing parts look brilliant and worked straight out of the box.

Room for improvement, but brilliant none the less

Easy to integrate modal with Login and Registration features.

Logical Captcha vs AJAX Login and Registration modal popup + inline form