BuddyPress.org

@famous
Redirect from what? It would help if you explained the criteria. Do you want logged in users redirected to their profile?

You can try this in bp-custom.php or your themes functions.php:

function bphelp_redirect_to_profile_on_login() {
global $bp;
if(!is_user_logged_in()) { 
wp_redirect( get_option('siteurl') . '/profile' );
}
}
add_filter('get_header','bphelp_redirect_to_profile_on_login',1);

Let me know if it works for you!
If you dont want to try this then use the plugin:
https://github.com/bphelp/private_community_for_bp
And change line 27 accordingly in private-community-for-bp.php to the page you want folks redirected too upon login before you activate the plugin.

@famous
To redirect to profile add the following code courtesy of @sbrajesh at BuddyDev to your bp-custom.php :

/*Make sure profile is default component*/
define('BP_DEFAULT_COMPONENT','profile');

/*let us filter where to redirect */
add_filter("login_redirect","bpdev_redirect_to_profile",10,3);
 
function bpdev_redirect_to_profile($redirect_to_calculated,$redirect_url_specified,$user)
{
if(empty($redirect_to_calculated))
$redirect_to_calculated=admin_url();
 
/*if the user is not site admin,redirect to his/her profile*/
if(!is_site_admin($user->user_login))
return bp_core_get_user_domain($user->ID );
else
return $redirect_to_calculated; /*if site admin or not logged in,do not do anything much*/
 
}

For logout use the following code also courtesy of @sbrajesh to redirect back to your home url:

add_filter('logout_url',"bpdev_logout_url",100,2);
function bpdev_logout_url( $logout_url, $redirect) {
//simply ignore the redirect and set it to the main domain
//let us check for buddyopress,if yes,let us get the bp root domain right ?
if(function_exists("bp_core_get_root_domain"))
$redirect=bp_core_get_root_domain();
else
$redirect = get_blog_option( SITE_ID_CURRENT_SITE, 'siteurl' );

$args = array( 'action' => 'logout' );
if ( !empty($redirect) ) {
$args['redirect_to'] = $redirect;
}

$logout_url = add_query_arg($args, site_url('wp-login.php', 'login'));
$logout_url = wp_nonce_url( $logout_url, 'log-out' );

return $logout_url;
}

It works for me. I tested it myself. Maybe you have some function in your theme, or plugins that is interfering with it. Have you tried basic troubleshooting by deactivating all plugins other than BP and activating twenty twelve theme or bp-default theme?

@famous
I have never used that widget but you can always drop the widget in the dashboard to the inactive widget section and then test if that is what is causing the login redirect function to fail.

@famous
That is a little strange. Are using mutisite? On a single site BP install the login/logout shows in the sidebar with the Meta Widget. Are you using a full width template? If so you can use this plugin to provide a login in the toolbar which I use with a full page template with WP 3.5.1 and BP 1.7.2 and it works, get it here:
https://wordpress.org/plugins/admin-bar-login/
Please provide as much info as you can on your install. If I can’t help, it will help others to help you. Thanks!

What did you want? BP used to provide a hardcoded sidebar login bp-me function, you can still find that in bp-default and copy it over to your theme, or grab this upgraded & extended version:
https://github.com/hnla/hnla-bp-sidebar-me.

@famous
Try this just make sure you follow the instructions in the commented code. Place it in bp-custom.php :

/* Redirects to profile upon login, and upon logout redirects to activity page unless changed in line 6 */
function bp_help_redirect_to_profile(){
 global $bp_unfiltered_uri;

 $bphelp_my_home_page = 'activity';  // WARNING: make sure you replace 'activity' in this line to the same thing you set dashboard/settings/reading front page to.

 if ( !is_user_logged_in() && ( $bp_unfiltered_uri[0] != $bphelp_my_home_page ) ) 
  bp_core_redirect( get_option('home') );

 elseif( is_user_logged_in() && ( $bp_unfiltered_uri[0] == 'activity') )
	bp_core_redirect( get_option('home') . '/members/' . bp_core_get_username( bp_loggedin_user_id() ) . '/profile' );

}
	
add_action( 'wp', 'bp_help_redirect_to_profile', 3 );

@famous
Use the last code because I made a slight change.

@famous
Try this out. This definitely works if you follow the instructions:
BuddyPress Redirect To Profile Trick Using A Landing Page.

vv

plugin at https://wordpress.org/plugins/bp-redirect-to-profile/ OR https://wordpress.org/plugins/bp-profile-as-homepage-fork/