you have to return the Observable

 return request
    .map((res: Response) => res.json())
    .catch((error: any) => {
        // todo: log?

        if (error.status == 500) {
            this.alertService.showError(error.statusText);
        } else if (error.status == 588) {
            this.alertService.showAlert(error.statusText);
        }

        return Observable.throw(error.statusText);
    });

Sometimes when you call catch without using arrow function like below

getUserList() {
    return this.http.get(this.constURL + '/api/url/here', this.headerOptions)
    .catch(this.handleError);
}

handleError(error: Response) {
    if (error.status == 500) {      
      this.router.navigate(['/login']);
    } else {
      return Observable.throw(error);
    }
}

then it gives error of

ERROR TypeError: Cannot read property 'navigate' of undefined not getting this

Because in handleError function this object is not accessible..if you console this.router then you will get undefined.. so this object not working and not getting router all available methods

So you have to use arrow function here like below

getUserList() {
    return this.http.get(this.constURL + '/api/url/here', this.headerOptions)
    .catch(error => { 
      return this.handleError(error);
    });
}

handleError(error: Response) {
    if (error.status == 500) {      
      this.router.navigate(['/login']);
    } else {
      return Observable.throw(error);
    }
}

Also if you have not mentioned return for handlerError function then it will throw error again like

Argument of type '(error: any) => void' is not assignable to parameter of type

So its necessary to type return for handlerError function.

Check here for in detail.He has explained code very well with all possible errors and solution of that..worked for me

This is an answer for angular 6 with RXJS 6. In your request function, it would look similar to this. Note that catch has been replaced with catchError and Observable.throw is now throwError. Also in RXJS 6 we use pipe to join together a sequence of function we wish to perform instead of the dot chaining previously.

//In your service

getData(url: string): Observable<any> {
    let options = this.getHTTPOptions();
    return this.http.get<any>(url, options).pipe(
          catchError( (err: any, caught: Observable<any>) => { return 
        throwError(this.generalErrorHandler(err, caught)) } ) );
}

Then you can have an error handler. The key is to specify the keyword return in both the catchError function above and return the error in the handler. The arrow ( => ) allows you to pass the context of the calling function into the error handler which means you can do cool things such as this.router.navigate(['someroute']); (If you have the router imported in your service)

//In your service

  generalErrorHandler(error: any, caught: Observable<any>): Observable<any> {
    console.log('error caught: ', error);
    if( error.error.status == "INVALID_TOKEN" || error.error.status == "MAX_TOKEN_ISSUE_REACHED"){
      console.log('token has expired');
      this.logout();
      return error;
    }
    return error;
  }

Some key imports to get this to work:

//Imports for the service

import { HttpClient, HttpHeaders, HttpErrorResponse } from '@angular/common/http';
import { Http, Response } from '@angular/http';
import { catchError, map } from 'rxjs/operators';
import { Observable, throwError, of} from 'rxjs';

And lastly to subscribe to the request to get your data:

//In your component, don't forget to import your service

let response$ = this.someService.getData('url here');
response$.subscribe( 
    data => { console.log('do stuff to data here', data); },
    err => { console.log("couldn't get data, maybe show error to user"); },
    () => { console.log('function that is called upon finish'); }
);